Name(s) ___________________________________________________ Hr ___
Type 2 Projectile Motion, In class work. Neglect air resistance.
1. Dustin Colquitt, the KC punter, the kick, has punted a 65 yard
punt. Let’s say that his punt has a velocity of 25 m/s and is directed
at an angle of 40 degrees above the horizontal. Determine (a) the
time of flight (hang-time), (b) the horizontal displacement (range),
and (c) the maximum height (altitude) of the football. Assume type
2 trajectory. Usually we round these to the nearest hundredths.
(answers: The football has a hangtime of 3.28 seconds, its range (delta x) is 62.8 meters which is approx. equal to 65 yards. Its max height
(delta y) occurs at the apex and involves half the time. You should get a height of around 13.17 meters.)
General physics, type 2 trajectory practice problems, p. 1
2. A trebuchet was a weapon used by medieval armies to tear down castle walls. It worked in a similar
way as a catapult except that with a trebuchet, a heavy weight was placed in the basket. This basket
would drop down sending the arm upward. At the end of the arm was a big rock or other object. The
object would go flinging forward as a projectile. The projectile would go over the castle wall or hit it
causing damage to the wall or the inhabitants in the castle. Here is a picture:
Given an initial velocity of 100 m/s at and angle of 60 degrees:
Determine the time of flight (t), range (delta x) and the maximum altitude (delta y) for the
projectile given.
(answers: The hangtime of the projectile is around 17.67 seconds. It travels forward around 883 or 884 meters depending upon
rounding and reaches a max height of around 382 or 383 meters.)
General physics, type 2 trajectory practice problems, p. 2
3. One of the most exciting things to watch at the circus is when a person is launched out of a cannon and
flies across the arena and lands safely on a net.
Emanuel Zacchini, a circus performer was one of the first human “cannonballs.” In 1939, he performed a
spectacular feat: he shot out of a cannon and soared over three Ferris wheels and then landed safely in a
net. In this case, Emanuel was launched with an initial speed of 26.5 m/s at an angle of 53 degrees as
measured from the horizontal. Each Ferris wheel was 18 meters high. Assume a type 2 parabola. See the
figure given:
(a) Find Emanuel’s hang time.
(b) Where should the safety net be placed?
(c) If Emanuel reached his maximum height directly over the middle Ferris wheel, by how many
meters did he clear it? (hint, find his delta y at the apex and subtract the height of the Ferris wheel.
(answers. Emanuel’s hang time is around 4.32 seconds. The safety net should be placed around 68.88 or 69 meters away.
What is his clearance? You should find his max altitude should be around 22.8 or 23 meters. Subtract 18 m from this and he
clears the ferris wheel by around 4.8 m (or around 5 meters).
General physics, type 2 trajectory practice problems, p. 3
4. This one works a bit differently but I have given you some hints…
One of the most incredible athletes to come out of Kansas is Kendra Wecker. Kendra still holds the state
record for the javelin throw (146.5 ft). In 2000, she competed in the Olympic trials in the javelin. She
attended KSU (Kansas State Univ), playing basketball, scoring 2,333 points, still a school record. She
also threw the javelin at KSU, and broke the school record with a throw of 179’9”. She now plays
professional basketball (WNBA) for the San Antonio Silver Stars.
Let’s analyze her throw of 179’9” throw (54.7 meters).
(a) If she throws the javelin 54.7 meters and it stays in the air for a total time of 2.25 seconds, what
velocity did the javelin have in the x direction (vix)? Hint…you are given the range of the javelin
and the total time.)
(b) Given that this throw was tossed at a launch angle (θ) = 36 degrees, what is the overall launch
velocity (initial velocity, vi)? Hint: you have the horizontal x velocity from the above problem and
you know the angle is 36 degrees so you can use cosine to get the initial velocity.
(c) Calculate the maximum height of the javelin (use apex time and the Δy equation).
(answers: the velocity in the x direction is 24.31 m/s. The overall velocity, vi = 30 m/s. The max height
of the javelin is around 13.6 meters.)
General physics, type 2 trajectory practice problems, p. 4