Physics11–’Kinematics0’Scalarvs.Vector...Runnata Gass is driving through town at 25.0 m/s and...

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Physics 11 – Kinematics Scalar vs. Vector -2 -1 0 1 2 3 4 5 6 7 8 A B Scalar quantities have only a magnitude (amount). Vector quantities have a magnitude and a direction. We represent them as arrows. Distance (d): the separation between two points. Is distance a scalar or a vector? _____________ Displacement (Δd): A measure of the change in position. Is displacement a scalar or a vector? ______________ Δd = final position – initial position. The sign of the value for indicates the direction. a) what is the distance of Car A from Car B? ___________ (scalar / vector) b) what is the distance of Car B from Car A? ___________ (scalar / vector) c) what is the position of Car A? ____________ (scalar / vector) of Car B? ____________(scalar / vector) d) what is the displacement of Car A measured from Car B? ________(s/v) e) what is the displacement of Car B measured from Car A? ________(s/v) Ex: A student walks 5 m east and then 3 m west. a) What is the distance (scalar) travelled? b) What is the student’s displacement (vector)? NOTE: When adding Vectors… Ex: A polar bear meanders 275 m east and then turns around and ambles 425 m west. a) What was the distance travelled by the bear? b) What was the bear’s displacement?

Transcript of Physics11–’Kinematics0’Scalarvs.Vector...Runnata Gass is driving through town at 25.0 m/s and...

Page 1: Physics11–’Kinematics0’Scalarvs.Vector...Runnata Gass is driving through town at 25.0 m/s and begins to accelerate at a constant rate of –1.00 m/s2. Eventually Runnata comes

Physics  11  –  Kinematics  -­‐  Scalar  vs.  Vector                                                                                                                                                                                                                          

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Scalar  quantities  have  only  a  magnitude  (amount).  

Vector  quantities  have  a  magnitude  and  a  direction.      We  represent  them  as  arrows.  

Distance  (d):  the  separation  between  two  points.      Is  distance  a  scalar  or  a  vector?    _____________  

Displacement  (Δd):  A  measure  of  the  change  in  position.        Is  displacement  a  scalar  or  a  vector?    ______________  

                                           Δd  =  final  position  –  initial  position.                    The  sign  of  the  value  for  indicates  the  direction.      

a)    what  is  the  distance  of  Car  A  from  Car  B?  ___________  (scalar  /  vector)  

b)  what  is  the  distance  of  Car  B  from  Car  A?  ___________  (scalar  /  vector)  

c)  what  is  the  position  of  Car  A?  ____________    (scalar  /  vector)                              of  Car  B?  ____________(scalar  /  vector)  

d)  what  is  the  displacement  of  Car  A  measured  from  Car  B?  ________(s/v)    

e)  what  is  the  displacement  of  Car  B  measured  from  Car  A?  ________(s/v)      

 

Ex:  A  student  walks  5  m  east  and  then  3  m  west.  

a)  What  is  the  distance  (scalar)  travelled?  

 

 

b)  What  is  the  student’s  displacement  (vector)?  

 

NOTE:  When  adding  Vectors…  

 

Ex:  A  polar  bear  meanders  275  m  east  and  then  turns  around  and  ambles  425  m  west.  

a)  What  was  the  distance  travelled  by  the  bear?  

 

 

b)  What  was  the  bear’s  displacement?  

 

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Describe  the  following  angles  Ex:  A  little  girl  takes  her  dog  for  a  walk  around  a  city  block  as  shown.  

 

a) What  is  the  distance  travelled?  

 

 

b) What  is  her  final  displacement?  

 

 

c) What  was  her  displacement  at  C?  

 

 

 

d) What  was  her  displacement  at  B?    

 

Add  each  of  the  following  vectors  and  find  the  total  resultant.  

1) 15  m  East  and  25  m  North  

 

 

 

2) 220.0  m  North  and  80.0  m  West  

 

 

 

3) 2.2  m  South  and  1.8  m  North  

 

 

 

4) 150  m  East  and  180  m  South  

 

 

 

5) 45.0  m  South  and  30.0  m  East  and  15.0  m  North    

 

 θ

 θ  θ

 θ

 θ

 θ

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Physics  11  –  Kinematics  -­‐  Speed  vs.  Velocity                                                                                                                                                                                                                        

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 Speed  (v):    

• Speed  is  a      

 

 Velocity  (v):    

• Velocity  is  a      

 

 

Where  Δ  means    

Ex:  A  student  travels  11  m  north  and  then  turns  around  and  travels  25  m  south.  If  the  total  time  of  travel  is  12  s,  find:  

a) The  student’s  average  speed.    

 

b) The  student’s  average  velocity.  

1)  How  long  does  it  take  a  car  traveling  at  45  km/h  to  travel  100.0  m?  

 

 

 

2)  How  far  does  a  skateboarder  travel  in  22  s  if  his  average  velocity  is  12.0  m/s?  

 

 

 

3)  A  shopping  cart  moves  from  a  point  3.0  m  West  of  a  flagpole  to  a  point  18.0  m  East  of  the  flagpole  in  2.5  s.    Find  its  average  velocity.    

 

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Average  Velocity  and  Speed    

1. A  high  school  bus  travels  240  km  in  6.0  h.    What  is  its  average  speed  for  the  trip?  (in  km/h)    

2. A  spider  travels  across  a  driveway  3.6  m  wide  with  a  speed  of  14  cm/s.    How  long  will  it  take  to  cross  the  driveway?    

3. Jay  Umpshot,  one  of  the  many  stars  of  the  local  basketball  team,  steals  the  ball  and  runs  the  length  of  the  court  in  8.5  seconds  at  a  speed  of  5.0  m/s.    How  long  is  the  court?    

4. If  a  car  is  traveling  at  25  m/s,  how  far  does  it  travel  in  1.0  hour?        

5. A  caterpillar  travels  across  the  length  of  a  2.00  m  porch  in  6.5  minutes.  What  is  the  average  velocity  of  the  caterpillar  in  m/s?    

6. A  motorist  traveling  on  a  straight  stretch  of  open  highway  sets  his  cruise  control  at  90.0  km/h.  How  far  will  he  travel  in  15  minutes?      

7. A  motorcycle  travels  90.0  km/h.  How  many  seconds  will  it  take  the  motorcycle  to  cover  2.10  x  103  m?    

8. A  hiker  is  at  the  bottom  of  a  canyon  facing  the  canyon  wall  closest  to  her.  She  is  280.5  m  from  the  wall  and  the  sound  of  her  voice  travels  at  340.0  m/s  at  that  location.  How  long  after  she  shouts  will  she  hear  her  echo.    

9. A  woman  makes  a  trip  to  a  nearby  shopping  mall  that  is  located  40.0  km  from  her  home.    On  the  trip  to  the  mall  she  averages  80.0  km/h  but  gets  a  speeding  ticket  upon  her  arrival.  On  the  return  trip  she  averages  just  40.0  km/h.  What  was  her  average  speed  for  the  entire  trip?    

10. A  cross-­‐country  rally  car  driver  sets  out  on  a  100.0  km  race.  At  the  halfway  marker  (50.0  km),  her  pit  crew  radios  that  she  has  averaged  only  80.0  km/h.  How  fast  must  she  drive  over  the  remaining  distance  in  order  to  average  100.0  km/h  for  the  entire  race?    

11. A  supersonic  jet  travels  once  around  the  earth  at  an  average  speed  of  1.6  x  103  km/h.    Its  orbital  radius  is  6.5  x  103  km.    How  many  hours  does  the  trip  take?    

 

 

 1)  4.0x101  km/h      2)  26  s      3)  43  m      4)  9.0x104  m    5)  5.1x10-­‐3  m/s      6)  23  km      7)  84.0  s    8)  1.650  s    

9)  53.3  km/h        10)  133  km/h      11)  26  h  

 A  motorist  travels  160  km  North  at  80.0  km/h  and  then  110  km  South  at  100.0  km/h.    What  is  the  average  speed  and  average  velocity  of  the  motorist  for  this  trip?    

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Physics  11  –  Kinematics  –  Uniform  Accelerated  Motion      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Acceleration:    

Ø Acceleration is a______________.

 Anytime  an  object’s...  

 

1) A  sprinter  starts  from  rest  and  reaches  a  speed  of  12  m/s  in  4.25  s.  Find  his  acceleration.  

 

 

 

 

2) A  car  starts  from  rest  and  accelerates  at  15  m/s2  for  3.0  s.  What  is  its  top  speed?    

 

 

 

 

3) If  a  snowboarder  is  traveling  at  8.0  m/s  how  long  will  it  take  her  to  reach  36.0  m/s  if  she  can  accelerate  at  a  rate  of  3.5  m/s2    

 

The  acceleration  of  an  object  can  be  found  with:  

 

 

Where:  

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Acceleration  Practice  

1) John  is  running  with  a  jet  pack  from  rest  and  accelerates  up  to  90.0  m/s  in  6.0  s.  What  is  John’s  acceleration?    (15  m/s2)      

2) Mackie  is  riding  a  high-­‐powered  train  that  accelerates  40.0  m/s2  for  3.0  min.  If  the  train  starts  at  rest,  what  is  the  train’s  final  velocity?   (7.2  x  103  m/s)  

 

3) If  Strawberry  Shortcake  accelerates  in  her  Muffin  Mobile  at  10.0  m/s2,  starting  from  rest,  and  her  finishing  speed  is  112  m/s,  how  long  did  her  trip  take?     (  11.2  s  )    

 

4) A  bird  is  buzzing  around  at  24  m/s.  The  bird  decides  to  accelerate  at  2.0  m/s2  for  8.0  s.  What  is  the  bird’s  final  velocity?       (4.0  x  101  m/s)  

 

5) A  bicycle  travels  at  18  m/s  then  comes  to  a  stop.  If  this  took  4.0  s,  what  was  the  bike’s  acceleration?                           (  -­‐4.5  m/s2  )  

 

6) Suzie  Lvkestaski  has  reached  the  end  of  the  ski  slope  and  abruptly  slows  from  29.0  m/s  to  1.80  m/s  in  1.45  seconds.  Determine  Suzie's  acceleration  rate  she  moved  during  this  braking  period.    (  -­‐  18.8  m/s2  )  

 

7) A  dragster  accelerates  from  rest  to  200.0  km/h  in  2.0  s.  What  is  its  acceleration  (28  m/s2)    

8) During  the  annual  shuffleboard  competition,  Renee  gives  her  puck  an  initial  speed  of  9.32  m/s.  Once  leaving  her  stick,  the  puck  slows  down  at  a  rate  of  -­‐4.06  m/s2.    Determine  the  time  it  takes  the  puck  to  slow  to  a  stop.  (2.30  s)  

 

9) A  rock  rolls  down  a  hill  with  an  acceleration  of  7.8  m/s2,  reaching  25  m/s  in  2.2  s.  What  was  its  initial  velocity?     (7.8  m/s)  

 

Motion      Velocity        Acceleration  A  car  sitting  at  a  stop  light  hits  the  gas  

   

From  rest  you  back  out  of  your  driveway  

   

A  plane  lands  and  comes  to  a  stop  

   

You  drop  a  rock  off  a  cliff  

   

 

You  throw  a  rock  straight  up  

   

 

Anytime  an  object’s  velocity  is  changing,  it  is  accelerating.  

Ø An  increase  in  velocity  is    

 

Ø A  decrease  in  velocity  is    

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Physics  11  –  Kinematics  –  Graphing  Motion    

 Sketch  each  of  the  following  situations:  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

For  d  vs.  t  graphs:  

� Slope  =        

       

 

For  v  vs.  t  graph:  

� Slope  =      

 

• Area  under  graph  =  

1)  A  hockey  player  skates  at  a  constant  speed  from  blue  line  to  blue  line.  

d  (m)  

            t  (s)  

 

 

v  (m/s)  

t  (s)  

2)  A  football  is  kicked  straight  up  and  then  falls  back  down.  

       d  (m)                 t  (s)    

 

   v  (m/s)  

                                                                                                                                                               t  (s)  

   

 

3)  A  swimmer  swims  the  length  of  a  pool  at  a  constant  speed,  quickly  turns  around  and  swims  back.  

 d  (m)                                                                                                                                                t  (s)    

 

v  (m/s)                      t  (s)    

4)  A  person  speeds  up  to  a  maximum  speed  then  travels  for  a  while  at  that  speed  

   

                 d  (m)                                                                                                                                                                  t  (s)    

       v  (m/s)                   t  (s)    

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1. Runnata Gass is driving through town at 25.0 m/s and begins to accelerate at a constant rate of –1.00 m/s2. Eventually Runnata comes to a complete stop. Represent Runnata's accelerated motion by sketching a velocity-time graph. Use the velocity-time graph to determine the distance traveled while slowing.

2. Otto Emissions is driving his car at 25.0 m/s. Otto accelerates at 2.0 m/s2 for 5.0 seconds. Otto then maintains this constant velocity for 10.0 more seconds. Represent the 15 seconds of Otto Emission's motion by sketching a velocity-time graph. Use the graph to determine the distance Otto traveled during the entire 15 seconds.

3. Chuck Wagon travels with a constant velocity of 0.50 m/s for 10.0 s. Chuck then accelerates at –0.25 m/s2 for 2.0

seconds. Sketch a velocity-time graph for Chuck Wagon's motion. Use the velocity-time graph to determine the total distance traveled by Chuck Wagon during the 12.0 seconds of motion.

4. Earl E. Bird travels at 30.0 m/s for 10.0 seconds. He then accelerates at 3.00 m/s2 for 5.00 seconds. Construct a

velocity-time graph for Earl E. Bird's motion. Use the plot to determine the total distance traveled.

Imagine  a  car  at  a  stop  light.  When  the  light  turns  green  it  accelerates  forward  at  a  constant  rate.  

Sketch  d  vs.  t,  v  vs.  t  and  a  vs.  t  graphs  of  its  motion.    

 

Tex  Ting  is  traveling  down  the  interstate  at  45.0  m/s  when  ahead  he  sees  an  accident  in  the  middle  of  the  road.    It  takes  Tex  1.5  s  to  recognise  the  danger  and  slam  on  the  brakes.    He  slows  down  at  a  rate  of  –15.0  m/s2.  Construct  a  velocity-­‐time  graph  for  Tex  Ting’s  motion  to  determine  the  distance  he  would  travel  prior  to  reaching  a  complete  stop.  

 

 

 

1)    313  m                        2)    5.0  x  102  m              3)    5.5  m              4)  488  m  

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Physics  11  –  Kinematics  –  Interpreting  Motion  Graphs                                                                                                                                                                                                                          

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Physics  11  –  Kinematics  –  The  Kinematics  Equations  of  Motion      

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

If  an  object  is  accelerating  then  the  formula:  

Gives  us  only  the  _______  ________  

We  can  also  find  average  velocity  using:  

       

1)      Ex:  A  squad  car  traveling  at  7.0  m/s  East  speeds  up  to  22.0  m/s  East  in  1.7  s.  What  is  its  acceleration?  

 

 

 

In  order  to  solve  problems  with  uniform  acceleration  we  need  to  use  3  formulae.  These  3  formulae  use  the  variables:  

vf    =    vo  =      a    =    Δd  =  `  t    =    

3)    Ex:  A  car  accelerates  from  15.0  km/h  at  2.00  m/s2.  How  far  has  it  traveled  when  it  reaches  30.0  km/h?  

 

2)      Ex:  A  sprinter  starts  from  rest  and  accelerates  uniformly.  He  travels  100.0  m  south  in  9.69  s,  what  was  his  average  acceleration?  

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Kinematic  Equations  

1.  A  ball  rolling  down  a  ramp  was  displaced  19.6  m  while  uniformly  accelerating  from  rest.  If  the  final  velocity  was  5.00  m/s.  what  was  the  rate  of  acceleration?  

2.  If  a  bullet  leaves  the  muzzle  of  a  rifle  at  600.0  m/s,  and  the  barrel  is  0.90  m  long,  what  was  the  acceleration  of  the  bullet  while  in  the  barrel?  

3.  The  Jamaican  bobsled  team  hit  the  brakes  on  their  sled  so  that  it  slows  at  a  uniform  rate  of  0.43  m/s².  How  long  does  it  take  to  stop  if  it  travels  85  m  before  coming  to  rest?  

4.  A  car  starts  from  rest  and  accelerates  uniformly  to  reach  a  speed  of  21  m/s  in  7.0  s.  What  was  the  speed  of  the  object  after  2.0  seconds?  

 

 

 

 

5.  A  bike  rider  accelerates  uniformly  at  2.0  m/s²  for  10.0  s.  If  the  rider  starts  from  rest,  calculate  the  distance  traveled  in  the  fourth  second.    (i.e.  between  t  =  3  s  and  t  =  4  s).  

 

6.  CHALLENGE:  A  driver  of  a  car  going  90.0  km/h  suddenly  sees  the  lights  of  a  barrier  40.0  m  ahead.  It  takes  the  driver  0.75  s  before  he  applies  the  brakes  (this  is  known  as  reaction  time).  Once  he  does  begin  to  brake,  he  slows  at  a  rate  of  10.0  m/s².  

a)  Does  he  hit  the  barrier?  

b)  SUPER-­‐CHALLENGE:  What  would  be  the  maximum  speed  at  which  the  car  could  travel  and  NOT  hit  the  barrier  40.0  m  ahead?  

 

 

Ex  1:    A  dragster  initially  at  rest  at  a  stop  light  hits  the  gas  and  reaches  100.0  km/h  in  3.2  s.?    

a.  What  is  its  acceleration?  

 

 

 

b.  How  far  does  he  travel  in  this  time?  

 

 

 

 

 

Ex  2:  A  ball  is  rolled  ramp  a  hill  at  3.6  m/s.  After  4.0  s  it  is  travelling  at  8.2  m/s.  How  far  did  it  roll?  

 

 

 

1)    0.638  m/s2        2)  2.0  x  105  m/s2        3)  2.0  x  101  s        4)  6.0  m/s      5)  7  m        6a)  YES!!      6b)    78  km/h  

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Physics  11  –  Kinematics  –  Acceleration  Due  to  Gravity      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

• In the absence of air friction…  

•Near Earth’s surface the acceleration is  

Example:  A  student  drops  their  homework  down  a  wishing  well.  After  2.4  s  it  hits  the  water  at  the  bottom.  How  deep  is  the  well?  

Example:  A  football  is  kicked  straight  up  in  the  air  at  15  m/s.  a)  How  high  does  it  go?    

 

 

 

b)  What  is  its  total  hangtime?    

 

Example:  A  student  stands  on  the  edge  of  a  45.0  m  high  cliff.  They  throw  their  physics  homework  straight  up  in  the  air  at  12.0  m/s.  a.    How  long  does  it  take  to  come  back  down  to  the  same  height  as  the  student?  

 

 

 

 

b.  If  it  falls  all  the  way  to  the  bottom  of  the  cliff,  how  fast  is  it  traveling  when  it  hits  the  ground?  

 

 

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1) Mario jumps straight upwards with a velocity of 14.0 m/s. What is his displacement of after 1.80 s? (9.32 m)

 

2) Luigi jumps straight upwards at 15.0 m/s. How high is he when he is travelling at:

a) 8.0 m/s upwards? (8.2 m) b) 8.0 m/s downwards? (8.2 m)

 

 

3) Sick of his guff, Optimus Prime decides to throw Megatron down off the top of a building at 5.0 m/s. Megatron hits the ground traveling at 32.0 m/s.

a) How long does it take to hit the ground?(2.8 s)

b) How far does he fall?(- 51 m)  

 

4) While strolling along on Planet X an astronaut decides to throw a hammer and a feather upwards at 5.0 m/s. They both return to the point of release in 3.0 s. What is the acceleration due to gravity on Planet X? (-3.3 m/s2)

 

 

5) Princess Toadstool stands on the edge of a 30.0 m high cliff. She throws Bowser upwards at 20.0 m/s. If Bowser falls all the way to the bottom of the cliff, find:

a) his velocity when he hits the ground. (-31.4 m/s)

b) the time it takes to hit the ground. (5.24 s)  

Acceleration  Due  to  Gravity    

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Physics  11  –  Kinematics  –  Horizontal  Projectile  Motion      

   

 

 

 

 

 

 

 

 

 

   

 

   

 

 

 

 

 

 

 

 

 

 

 

 

Remember  that  the  x  and  y-­‐components  are  _______________  and  therefore  totally  _______________.      

X-­‐components  

There  is  no  ________________  working  on  the  projectile  in  the  X  and  the  acceleration  is  always  _____________.  Therefore  the  only  equation  we  can  ever  use  is:  

The  only  value  that  can  ever  be  used  on  both  sides  is  ____________  because  it  is  a  ______________  .  

Y-­‐components  

In  this  case  there  is  always  a  constant  acceleration  of  _______________________.    Because  of  this  we  need  to  use  the  _______________________.    

 

Horizontal  Projectile  Problem:  A  student  sits  on  the  roof  of  their  house,  which  is  12  m  high.    She  can  launch  water-­‐balloons  from  a  slingshot  at  14.0  m/s.    If  she  fires  a  water-­‐balloon  directly  horizontally:  

a.  How  long  will  it  be  airborne?        This  depends  on:  

 

 

 

b.  How  far  forward  will  it  travel?            This  depends  on:  

 

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Horizontal  Projectile  Problems  

1.   A  rock  is  thrown  horizontally  from  the  top  of  a  cliff  98  m  high,  with  a  horizontal  speed  of  27  m/s.  

(a) For  what  interval  of  time  is  the  rock  in  the  air?    (b) How  far  from  the  base  of  the  cliff  does  the  rock  land?    (c) With  what  velocity  does  the  rock  hit?    

 2.   A  rescue  pilot  wishes  to  drop  a  package  of  emergency  supplies  so  that  it  lands  as  close  as  possible  to  a  target.  If  the  

plane  travels  with  a  velocity  of  81  m/s  and  is  flying  125  m  above  the  target,  how  far  away  (horizontally)  from  the  target  must  the  rescue  pilot  drop  the  package?    

3.   A  bullet  is  fired  with  a  horizontal  velocity  of  330  m/s  from  a  height  of  1.6  m  above  ground.  Assuming  the  ground  is  level  how  far  from  the  gun  will  the  bullet  hit  the  ground?    

4.   A  firefighter  is  standing  on  top  of  a  building  20.0  m  high.  She  finds  that  if  she  holds  the  hose  so  that  water  issues  from  it  horizontally  at  12  m/s,  the  water  will  hit  a  burning  wall  of  an  adjacent  building  at  a  height  of  15.0  m  above  the  ground.  What  is  the  horizontal  distance  from  the  firefighter  to  the  building?    

 5.      An  arrow  is  fired  horizontally  with  a  speed  of  25.0  m/s  from  the  top  of  a  150.0-­‐m-­‐tall  cliff.   Assuming  no  air  

resistance,  determine  the  distance  the  arrow  will  drop  in  2.50  s.      6.      A  skier  leaves  the  horizontal  end  of  a  ramp  with  a  velocity  of  25.0  m/s  [E]  and  lands  70.0  m  from  the  base  of  the  

ramp.  How  high  is  the  end  of  the  ramp  from  the  ground?        

 

Example:  A  Cutlass  Supreme  drives  straight  out  of  a  parking  garage  at  8.0  m/s  and  hits  the  water  3.4  s  later.  

a.  How  far  did  the  car  fall?  

 

 

 

 

b.  What  was  his  total  impact  velocity?  (magnitude  and  direction)  

 

 

 

         1)  a.  4.5  s      b.  120  m        c.  51  m/s  58o  BTH        2)  410  m            3)190  m          4)  12  m                    5)  30.7  m                        6)  38.5  m