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Physics 8A - Week 3 - 2D
Kinematics and Projectile
Motion:Solutions + detailed
rationales
Problem 1: Velocity Decomposition
A projectile is fired into the air with an initial speed of 10 m/s at an
angle of 30◦ with the horizontal.
Find the components of the initial speed in the x- and y-directions.
Figure 1: Trajectory of a Ball
Solution
Using trigonometry, we decompose the velocity vector:
√
◦ vix = vi
cos(30 ) = 5 3 m/s,
viy = vi sin(30◦) = 5
m/s.
Thus, the velocity vector is: √
vi = (5 3ˆi + 5ˆj) m/s.
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Problem 2: 1D constant acceleration
Suppose William wants to avoid a ticket for running a red light (the
following does not work legally and is not recommended). If the
speed of light is 300 m/s and he travels towards the traffic light at a
speed of 50 m/s, the light he perceive will be blue shifted and the
traffic light will appear green. He reaches this speed (50 m/s) from
rest over 1 km at constant accceleration.
(a) There are speed cameras at the 300 m and 400 m mark
(assuming he starts at 0 m) which take photos as he passes by.
How much time has passed between the two photos?
The car is accelerating at a constant rate from 0 to 50 m/s over
1km. Using the equation of motion, we must first find
acceleration to characterize the motion
Now that we know acceleration, we can write the displacement
of the car between any two times
To find the delta time, we need to find the initial velocity when
the car passed 300m. Using the same equation as earlier,
(b) There’s a speed camera in 200 m from his current position (1 km)
and he doesn’t want to get a third speeding ticket, so he
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Physics 8A - Week 3 - 2D
Kinematics and Projectile
Motion:Solutions + detailed
rationales
Problem 1: Velocity Decomposition
A projectile is fired into the air with an initial speed of 10 m/s at an
angle of 30◦ with the horizontal.
Find the components of the initial speed in the x- and y-directions.
Figure 1: Trajectory of a Ball
Solution
Using trigonometry, we decompose the velocity vector:
√
◦ vix = vi
cos(30 ) = 5 3 m/s,
viy = vi sin(30◦) = 5
m/s.
Thus, the velocity vector is: √
vi = (5 3ˆi + 5ˆj) m/s.
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Problem 2: 1D constant acceleration
Suppose William wants to avoid a ticket for running a red light (the
following does not work legally and is not recommended). If the
speed of light is 300 m/s and he travels towards the traffic light at a
speed of 50 m/s, the light he perceive will be blue shifted and the
traffic light will appear green. He reaches this speed (50 m/s) from
rest over 1 km at constant accceleration.
(a) There are speed cameras at the 300 m and 400 m mark
(assuming he starts at 0 m) which take photos as he passes by.
How much time has passed between the two photos?
The car is accelerating at a constant rate from 0 to 50 m/s over
1km. Using the equation of motion, we must first find
acceleration to characterize the motion
Now that we know acceleration, we can write the displacement
of the car between any two times
To find the delta time, we need to find the initial velocity when
the car passed 300m. Using the same equation as earlier,
(b) There’s a speed camera in 200 m from his current position (1 km)
and he doesn’t want to get a third speeding ticket, so he
FOR MORE EXAMS
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