Lecture 6: Vectors & Motion in

2 Dimensions (part II)

Questions of Yesterday

2) Two projectiles are thrown with the same initial speed, one at an angle with respect to the ground and the other at an angle 90o - . Both projectiles strike the ground at the same distance from the projection point. Are both projectiles in the air for the same length of time?

a) YESb) NO

1) A heavy crate is dropped from a high-flying airplane as it flies directly over your shiny new car? Will your car get totaled?

a) YESb) NO

Relative Velocity

Frame of Reference is important when measuringdisplacement, velocity & acceleration

60 mi/h

Most reference frames are stationary with respect to earthSpeed of moving object the same in any fixed reference frame

What if your reference frame is moving?

Relative Velocity

Frame of Reference is important when measuringdisplacement, velocity & acceleration

60 mi/h50 mi/h

Relative Velocity = Velocity of a moving object as measured by an observer

in frame of reference

Velocity of moving object relative to reference frame

Relative Velocity

60 mi/h50 mi/h

vCA = velocity of C as measured by A = 60 mi/hvBA = velocity of B as measured by A = 50 mi/hvCB = velocity of C as measured by B = 10 mi/h

0 mi/h

A

B C

vCB = vCA - vBA

Relative Displacement in 2 Dimensions

rAB = rAE - rBE

A & B = moving objects/reference framesE = stationary reference frame with respect to Earth

x

y

E

ArAE

Vector points

TO

Vector points FROM

Relative Displacement in 2 Dimensions

rAB = rAE - rBE

x

y

r AE

E

A

BrBE

rAB

Relative Velocity in 2 Dimensions

rAB = rAE - rBE

x

y

r AE

E

A

BrBE

rABv = r

t

rAB = rAE - rBE

t t t

vAB = vAE - vBE

Relative Velocity in 2 Dimensions

rAB = rAE - rBE

vy

v AE

E

A

Bv

BE

vAB

v = rt

rAB = rAE - rBE

t t t

vAB = vAE - vBE

vx

Relative Velocity in 2 Dimensions

vBA = - vAB

vAB = vAE - vBE

vy

v AE

E

A

Bv

BE

vAB

vx

vBA = vBE - vAE

vBA = -(vAE - vBE)

vy

v AE

E

A

Bv

BE

vB

A = -v

AB vx

Problem #1

An airplane that normally has a speed of 100 km/h through air is caught in a 100-km/h crosswind blowing from west to east, what will its velocity be relative to

the ground when its nose is pointed north in the crosswind?

Problem #2

A canoe is paddled at 4 km/h directly across a river that flows 3 km/h.

What is the resultant speed of the canoe?

How fast and in what direction can the canoe be paddled to reach a destination directly across the river?

Problem #3An airplane is flying horizontally with speed 1000 km/h (280 m/s) when an engine falls off. If it takes 30 s for

the engine to hit the ground:

How high is the airplane when the engine falls?

How far horizontally does the engine travel while it falls?

What is the engine’s velocity right before it hits the ground?

If the airplane somehow continues to fly as if nothing had happened, where is the engine relative to the

airplane at the moment the engine hits the ground?

What is the engine’s velocity relative to the airplane?

Problem #4

A homerun is hit in such a way that the baseball just clears a wall 21 m high, located 130 m from home

plate. The ball is hit at an angle of 35o to the horizontal. Assume that the ball is hit at a height of

1.0 m above the ground. Find:

a) the initial speed of the ball

b) the time it takes the ball to reach the wall

c) the velocity components and the speed of the ball when it reaches the wall

Questions of the Day1) A ball is thrown vertically upwards in the air by a

passenger on a train moving with a constant velocity. To a stationary observer outside the train, is the velocity of the ball at the top of its trajectorya) greater than

b) Less thanc) Equal tothe velocity observed by the passenger?

1) The hang-time of a basketball player who jumps a vertical distance of 2 ft is about 2/3 second. What will the hang-time be if the player reaches the same height while jumping 4 ft horizontally?a) less than 2/3 sb) greater than 2/3 sc) equal to 2/3 s