Homework #7: Projectile Motion
Instructions: Answer the following projectile motion questions. Show your work clearly, including a
description or drawing of your coordinate system (origin, positive directions for x & y). Start with a
general physics equation, solve it using symbols, and put the numbers in at the very end. Write your
final answers with the correct number of significant figures.
- A small marble rolls horizontally with speed vo off the top of a
platform 2.75 m tall, and it feels no appreciable air resistance. On
the level ground, 2.00 m from the base of the platform, there is a
1.50-m wide hole in the ground.
a. What initial speed would cause it to hit the left edge of
the hole?
b. What initial speed would cause it to hit the right edge of
the hole? - A soccer player kicks a ball at a speed of 74.0 miles per hour at an angle of 23.2o up from horizontal.
The ball lands at the same height from which it started. How long is the ball in the air? How far
does it travel horizontally before it lands? - A quarterback throws a football with initial velocity components voy = 10.0 m/s (upward) and
vox = 15.0 m/s (down the field). It is caught at the same height it is thrown from.
a. How long does it take for the football to reach its maximum height?
b. How high is this point above where the ball was released?
c. How much time, after it was thrown, elapses before the ball is caught? Compare this time
to what you found in part (a).
d. How far away from the quarterback is the ball when it is caught? - Repeat question 3, but have the initial speed of the ball be 22.0 m/s and the initial angle be 25.0o up
from horizontal. - A shot putter throws a 16-lb steel ball (a shot), releasing it at an unknown height above the ground
with an initial velocity of 11.2 m/s at an angle of 49.1o above horizontal. The shot lands on the
ground 1.85 s later.
a. What are the horizontal and vertical components of its initial velocity?
b. What is its maximum height above the ground?
c. How far, horizontally, did the shot travel before hitting the ground?
d. What are the horizontal and vertical components of its final velocity, right before it hits the
ground?
e. What are the magnitude and angle of the final velocity vector, right before the shot hits the
ground? - Each of the questions below refers to a projectile that is launched from the top of a tower, 45.0 m
above the ground, at a speed of 11.0 m/s at an angle of 36.5o up from horizontal.
a. Draw a diagram of the situation, labeling all of the known quantities. Also, use a dashed line
to sketch in the path of the projectile from its launch until it hits the ground.
b. Find the x and y components of its initial velocity.
c. How long does it take to reach its maximum height?
d. How high is its maximum height above the ground?
e. How long is it in the air before it hits the ground?
f. How far away from the base of the tower does it hit the ground?
g. Find the x and y components of its velocity right before it hits the ground.
h. Find its speed right before it hits the ground.