Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only...
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Transcript of Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only...
![Page 1: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/1.jpg)
Chapter 7Projectile Motion
![Page 2: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/2.jpg)
Projectile Motion• The motion of an object
that has been thrust into air where the only forces acting on it are gravity & air resistance.
![Page 3: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/3.jpg)
Projectile Motion•Because we ignore air resistance, the only force acting on thrown objects is gravity.
![Page 4: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/4.jpg)
Projectile•The object that has been given an initial thrust, fired, or thrown into air.
![Page 5: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/5.jpg)
Trajectory
•The path of a projectile as it travels
through space.
![Page 6: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/6.jpg)
In Projectile Motion•The vertical & horizontal components act independently & can be solved independently
![Page 7: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/7.jpg)
In Projectile Motion•The only force acting vertically is the force of
gravity causing downward acceleration.
![Page 8: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/8.jpg)
In Projectile Motion•There are no net forces acting horizontally; thus, the horizontal velocity is
constant.
![Page 9: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/9.jpg)
In Projectile Motion•Use your velocity formulas to solve for vertical & horizontal
motion independently.
![Page 10: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/10.jpg)
In Projectile Motion•Solve for time in air 1st
•Always use the vertical component to solve for the time in air.
![Page 11: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/11.jpg)
In Projectile Motion
•After solving for the time in air, solve for the range or horizontal distanced traveled
![Page 12: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/12.jpg)
A rock has been thrown horizontally at 4.0 m/s
from a tower 49 m high. Calculate: tair, dH, and vH & vV the instant before
impact:
![Page 13: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/13.jpg)
A bullet exits a 0.50 m barrel horizontally at
1000.0 m/s from a height of 2.0 m. Calculate: abullet
in barrel, tin barrel, tair ,vV at impact, dH:
![Page 14: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/14.jpg)
A plane flying horizontally at 250 m/s at an altitude of 4.9 km high drops a bomb. Calculate: tair, dH, and vV the
instant before impact:
![Page 15: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/15.jpg)
A ball rolls at 75 cm/s off the edge of a 49 cm
table. Calculate: tair, dH, and vV the instant
before impact:
![Page 16: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/16.jpg)
A car traveling at 1500 cm/s goes off the edge of a 0.49 km high cliff. Calculate: tair, dH, and
maximum vV:
![Page 17: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/17.jpg)
A car accelerates at 5.0 m/s2 for 250 m before
going off the edge of a 0.49 km high cliff. Calculate: t & max v on the ground, &
t, dH, and max vV in air:
![Page 18: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/18.jpg)
A cannon ball is fired at 1000.0 m/s at 53o from horizontally. Calculate: max height, tair ,vV at impact,
dH:
![Page 19: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/19.jpg)
Repeat the last problem with a cannon ball
exiting the barrel at the same speed with angles
of 40o, 45
o, & 50
o
![Page 20: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/20.jpg)
Assumming all factors are the same for that cannon, Calculate its
maximum range:
![Page 21: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/21.jpg)
A ball is thrown at 25 m/s at 45o from
horizontal. Calculate: tair, maximum height, vV at
impact, dH:
![Page 22: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/22.jpg)
A 25 Mg car is accelerated from rest at 5.0 m/s2 up a 250 m ramp at 37o from
horizontal. Calculate: t, & vf on the ramp, and dV, dH, t, and maximum vV in air:
![Page 23: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/23.jpg)
A 1.0 Mg block slides from rest down a 250 m ramp ( = 0.20) at 37o from horizontal that ends 490 m above the
ground. Calculate: t, & vf on the ramp, and dH, t, and
maximum vV in air:
![Page 24: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/24.jpg)
Review
![Page 25: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/25.jpg)
A sled coasts off a 0.49 km cliff at
18 km /hr.Calculate: tair, max
vV, & dH:
![Page 26: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/26.jpg)
A catapult launches a 250 kg rock at 100.0
m/s at 37o from horizontal. Calculate:
tup, dV, tair, & dH :
![Page 27: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/27.jpg)
Define each of the following
•DistanceDisplacement
•Speed Force
•Velocity Acceleration
![Page 28: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/28.jpg)
Give Units for each of the following
•DistanceDisplacement
•Speed Acceleration
•Velocity Force
![Page 29: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/29.jpg)
vf = vi + at
d = vit + ½ at2
vf2 = vi
2+ 2ad
![Page 30: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/30.jpg)
ProjectileMotion
ProjectileTrajectory
![Page 31: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/31.jpg)
A 25 Mg sled slides from rest down a 500.0 m slope ( = 0.10) at 37o from horizontal that ends 2.45 km above the ground. Calculate: t, & vf on the slope, and dH, tair, and the
maximum vV in air:
![Page 32: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/32.jpg)
A 250 Mg sled accelerates at 3.0 m/s2 up a 250 m ramp ( = 0.25) at 53o
from horizontal. Calculate: Fa, tramp, vf ramp,
tair, dv, & dH
![Page 33: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/33.jpg)
A 0.10 Mg cycle is accelerated with a force of 500.0 N for 10.0 s before hitting a 25 m ramp at 37o from horizontal.
Draw the system and Calculate: v at bottom & top of ramp, and t, dv, & dH in the air
![Page 34: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/34.jpg)
An airplane is flying horizontally due west at
360 km/hr at an altitude of 0.49 km & drops a 2000 lb
bomb. Draw the system and Calculate: tair,
maximum vV, & dH.
![Page 35: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/35.jpg)
A 50.0 kg person skis ( = 0.010) down a 3.0 km ski trail with an average slope of 30o. Draw the system
and Calculate: a, t, maximum v on the trail
![Page 36: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/36.jpg)
British Ships had cannons with muzzle velocities of 400 m/s
while the cannons at Ft McHenry could fire at 500 m/s. The British
could elevate to 45o while the Americans could elevate to 18o. Which cannons had the greater
range.
![Page 37: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/37.jpg)
Expanding gases produce about 10,000 N of force in a gun barrel.
One nation wants to build a cannon that will deliver a 2,000 kg cannon ball 200 km. Calculate the
length that the barrel must be. Because you are estimating round
g to –10 m/s2.
![Page 38: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/38.jpg)
AB
= 37o
= 53o
Y = 1.00 kN
XY
C
![Page 39: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/39.jpg)
AB
C
FH of AFH of B
WYWx + FV of C
FH of C
FH of C
FV of A FV of B +FV of C
![Page 40: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/40.jpg)
AB
C FH of B
WYWx + FV of C
FH of C
FH of C
FV of AFV of B
FV of C
FV of C
FH of A
![Page 41: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/41.jpg)
A 200.0 kg rock is catapulted at 53o from horizontal at about
0.10 km/s. Draw the system and Calculate: t, dv, & dH in
the air
![Page 42: Chapter 7 Projectile Motion. The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649cb05503460f949755a6/html5/thumbnails/42.jpg)
A rock is thrown at 37o from horizontal at about 25 m/s.
Draw the system and Calculate: t, dv, & dH in the air