Transcript Physics 1A: Introduction to Physics and Problem Solving

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 q with respect to the ground and the other at an
angle 90o - q. 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) YES
b) 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) YES
b) NO
Relative Velocity
Frame of Reference is important when measuring
displacement, velocity & acceleration
60 mi/h
Most reference frames are stationary with respect to earth
Speed 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 measuring
displacement, velocity & acceleration
50 mi/h
60 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
B
C
A
50 mi/h
0 mi/h
60 mi/h
vCB = vCA - vBA
vCA = velocity of C as measured by A = 60 mi/h
vBA = velocity of B as measured by A = 50 mi/h
vCB = velocity of C as measured by B = 10 mi/h
Relative Displacement in 2 Dimensions
rAB = rAE - rBE
A & B = moving objects/reference frames
E = stationary reference frame with respect to Earth
y
rAE
Vector
points
TO
A
Vector
points
FROM
E
x
Relative Displacement in 2 Dimensions
rAB = rAE - rBE
y
A
E
x
B
Relative Velocity in 2 Dimensions
y
rAB = rAE - rBE
v=
Dr
Dt
DrAB = DrAE - DrBE
Dt
Dt Dt
vAB = vAE - vBE
A
E
x
B
Relative Velocity in 2 Dimensions
rAB = rAE - rBE
v=
vAB = vAE - vBE
Dr
Dt
vy
A
DrAB = DrAE - DrBE
Dt
Dt Dt
E
vx
B
Relative Velocity in 2 Dimensions
vBA = vBE - vAE
vAB = vAE - vBE
vBA = -(vAE - vBE)
vy
vy
A
vBA = - vAB
A
E
vx
B
E
vx
B
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 #3
An 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 Day
1) 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 trajectory
a) greater than
b) Less than
c) Equal to
the 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 s
b) greater than 2/3 s
c) equal to 2/3 s