Name (s) _____________________________________________________ Hr. ___
General Physics, type 3 trajectories.
1. Let's do a field goal problem. In 1998, Jason Elam, the kicker for the Denver Broncos, tied an NFL
record by kicking a 63 yard field goal. The ball was placed approximately 66.75 meters away from the
goal post (this is 63 yards + 10 yards of endzone to goal). The crossbar of the goal is 3 meters high.
Let’s say that the ball was kicked from the ground (yi = 0 m) at 26.566 m/s at a
theta of 40 degrees.
First resolve your initial velocity into x and y components using cosine and sine.
(a) Determine the time it takes for the football to travel from the kicker’s foot
to the goalpost 66.75 meters away. [hint, use your x equation: Δx = vx(t)]
(b) What was the height of the ball at the position of the goal post? By how far
did the football clear the goalpost’s crossbar? (use your how far vertical equation
Δy = viy(t) + ½ (a)(t2) and solve for delta y. Remember that the crossbar
is 3 m high]
Delta x = 66.75 m
(answers. You should get around 3.28 seconds for the ball to reach the goalposts. At this point in time, it
is about 3.3 meters above the crossbars. The crossbar is 3 meters above the ground so the football clears
the crossbar by around 0.3 meters).
General physics, type 3 trajectories, p. 1
2. A tennis player hits a ball 2 m above the ground. The ball leaves his racquet with a speed of 10
m/s at an angle of 15 degrees above the horizontal. The horizontal distance to the net is 7 m and the
net is 1 m high. Does the ball clear the net? If so, by how much?
Ball is hit 2 m above ground
Net is 1 m above ground
(answer: tennis ball does clear the net by around 0.32 m)
General physics, type 3 trajectories, p. 2
3. In a fit of temporary insanity, a student throws his physics book off of the roof with a
speed of 10 m/s at an angle of 30 degrees above the horizontal. The ball is thrown
from a height of 11 m above the ground. Find the answers to the following questions.
a.
What is the ball’s initial velocity in the x direction (hint: vi∙cosθ)? (answer = 8.66 m/s)
b.
What is the ball’s initial velocity in the y direction (hint: vi∙cosθ)? (answer = 5 m/s)
c. How long does it take (seconds) for the ball to reach the apex after it is launched (hint, use your how fast equation
vertically, you know the ball stops vertically at the apex)? (answer = 0.51 s)
d. What is the total time (seconds) of the ball’s flight (launch to when it hits the floor) (hint: use the how far equation,
vertically, you know that the ball hits 11 m BELOW where it started) [note: you will use the quadratic equation here]?
(answer = 2.1 s)
e. What is the maximum height (meters) the ball will get above the roof? (hint, you will use the how far vertically
equation with your time from part c, this represents the position of the ball at that time) (answer = 1.28 m)
f. What is the ball’s range (horizontal displacement, Δx) from the edge of the roof? (hint, use your how far horizontal
equation with your total time) (answer = 18 m)
g. What is the ball’s final velocity (impact velocity) in the y direction? (hint, use your how fast equation vertically
with the total time) (answer = -15.6 m/s)
h. What is the ball’s final velocity (impact velocity) in the x direction? (hint, this is just the answer to part a as the
velocity is not changing in the x direction) (answer = 8.66 m/s)
i. Now, using the ideas from the previous two questions, what is the ball’s impact velocity vector (magnitude and
angle). Give the angle as reference from the horizontal. (use Pythagorean theorem for your answers to g and h and use
inverse tan also with g and h.) (answers = 17.8 m/s, 61 degrees below horizontal)
11 m
General physics, type 3 trajectories, p. 3
4. As a kid, I played T-ball. Do you know what T ball is? You put the ball on a T and the kids hit from
that. It usually is played by kids before they start Little League.
Let’s say that the baseball is hit from the T at a theta of 24 degrees. The T is 1
meter above the ground.
The initial velocity given to the ball is 26.6 m/s.
The ball flies into the gap between center and left field and hits the ground.
a) What is the time of flight of the ball? (answer: t = 2.29 or around 2.3 sec)
(HINT: you will use the how far vertically and you will use the quadratic
equation)
b) How far did the ball travel forward (delta x)? (answer: delta x = 55.6 or 56 meters)
(HINT: you will use your how far horizontal equation and solve for delta x)
General physics, type 3 trajectories, p. 4