Sample Projectile Problems

1. At Boston's Fenway Park, it is 310 feet (94.5 m) from homeplate to the left field wall The Green Monster which is 30 feet (9.2 m) high. If a batter hits a baseball at an initial height of 0.9 m, given the following velocities, does it clear the wall, hit the wall, or fall short?

a. v_x = 25 m/s, v_yo = 25 m/s [h = 25.32 m, clears]

b. v_x = 25 m/s, v_yo = 20.5 m/s [h = 8.31 m, hits wall]

c. v_x = 16 m/s, v_yo = 28 m/s [h = -4.83 m, falls short]

d. v_x = 14.1 m/s, v_yo = 47 m/s [h = 95.61 m, clears]

2. A football player attempts a 40 yard (36.58 m) field goal. The goal post cross bar is 10 feet
(3.048 m) above the field. If the ball is kicked from the ground, what is it's height when it reaches the crossbar, given the following velocity components?

a. v_x = 15 m/s, v_yo = 15 m/s [h = 7.41 m]

b. v_x = 17 m/s, v_yo = 12 m/s [h = 3.11 m]

c. v_x = 17 m/s, v_yo = 11.97092 m/s [h = 3.048 m]

3. Scottie Pippen lobs the ball to Michael Jordan so that MJ can do an Alley-Oop. If Scottie is 60 feet (18.29 m) away and releases the ball from a height of 2 m, and MJ has a maximum vertical reach of 11 feet (3.35 m), will MJ be able to reach the following lobs?

a. v_x = 15 m/s, v_yo = 7 m/s [h = 3.24 m, reaches]

b. v_x = 14 m/s, v_yo = 8 m/s [h = 4.08 m, misses]

4. A football is kicked from the ground with a velocity of 38 m/s at an angle of 40º degrees, and eventually lands at the same height. What is the direction and magnitude of the ball's velocity 0.2 seconds after impact? [v = 36.77 m/s, q = 37.66º] How far away does the ball land from the place it was kicked? [x = 144.97 m]

5. A high jumper leaves the ground with a vertical velocity of 6.3 m/s and a horizontal velocity of
2.2 m/s. Takeoff height = 0.8 m, landing height = 0.33 m. Find time of flight and range.
[t = 1.35 s, x = 2.97 m]

6. A pole vaulter takes 1.3 seconds to fall from peak height to the landing mat. What is his vertical velocity at contact with the mat? [v_yf = -12.75 m/s]

7. A diver leaves the springboard with a vertical velocity of 5.7 m/s, a horizontal velocity of 1.2 m/s, and a height of 3.49 m. How long will it take her to return to the same height? What horizontal range will she cover in this time? What is her velocity when she hits the water (h = 0.36 m)? [t = 1.16 s,
x = 1.39 m, v_yf = -9.69 m/s]

8. A golf ball is hit from a tee with a height of 3 m and lands on an elevated green with a height of 14 m, a horizontal velocity of 28 m/s, and a vertical velocity of -18 m/s. How far away from the tee does the ball land? [x = 117.6 m]

9. A ski jumper takes off from the ramp with an initial height of 40 m, a horizontal velocity of 32 m/s, and a vertical velocity of 11 m/s, landing with a final height of 1.5 m. What is the direction of the takeoff velocity vector, the vertical velocity at landing, and the horizontal range? [q = 18.97º, v_yf = -29.6 m/s,
x = 132.48 m]

10. An ice skater completes a triple axle. If her takeoff height was 1.4 m, and her peak height was 1.7 m, what was her vertical velocity at takeoff? How long did it take her to reach peak height?
[v_yi = 2.43 m/s, t = 0.25 s]

11. A shot put is released from a height of 1.7 m, with a velocity of 11.6 m/s at an angle of 39º. Find the range and vertical velocity at ground contact. [x = 15.23 m, v_yf = -9.31 m/s]

12. A baseball is hit at an initial height of 0.8 m, and reaches a peak height of 34 m. What was the vertical velocity of the ball at takeoff? How long did it take to reach peak height? [v_yi = 25.52 m/s,
t = 2.6 s]

13. A diver hits the water with a vertical velocity of -12.3 m/s at a final height of 1.2 m. What was her peak height? How long did it take to fall from her peak height to the water? [h = 8.9 m, t = 1.25 s]

14. A water balloon is launched with a velocity of 46 m/s at 40º with an initial height of 0.8 m. The balloon smashes into a building 15 m away from the launch point. Find the following information at the moment of impact with the building: horizontal and vertical velocity, height, time from launch to impact, and direction of balloon's velocity vector. [v_y = 25.35 m/s, v_x = 35.24 m/s, h = 12.61 m, t = 0.43 s,
q = 35.73º]

15. A diver has a vertical velocity of -12 m/s when she is 1.8 m above the water. What was her peak height? [h = 9.14 m]

16. A football falls from a peak height of 19 m and lands on the ground. What was the vertical velocity of the ball at impact? How long did it take to fall to the ground? [v_yf = -19.31 m/s, t = 1.97 s]

17. A golf ball travels a distance of 85 m, taking off and landing at the same height. If the ball was in the air 4 seconds, find the horizontal, vertical, and resultant velocities of the ball at takeoff. Also find the direction of the resultant velocity vector. [v_x = 21.25 m/s, v_y = 19.62 m/s, v = 28.92 m/s, q = 42.7 º]

18. A javelin lands with a final height of 0.5 m, a horizontal velocity of 19 m/s, and a vertical velocity of -21 m/s. If the javelin was released from a height of 1.6 m, how far did it travel? [x = 80.37 m]

a.	v_x = 25 m/s, v_yo = 25 m/s	[h = 25.32 m, clears]
b.	v_x = 25 m/s, v_yo = 20.5 m/s	[h = 8.31 m, hits wall]
c.	v_x = 16 m/s, v_yo = 28 m/s	[h = -4.83 m, falls short]
d.	v_x = 14.1 m/s, v_yo = 47 m/s	[h = 95.61 m, clears]

a.	v_x = 15 m/s, v_yo = 15 m/s	[h = 7.41 m]
b.	v_x = 17 m/s, v_yo = 12 m/s	[h = 3.11 m]
c.	v_x = 17 m/s, v_yo = 11.97092 m/s	[h = 3.048 m]

a.	v_x = 15 m/s, v_yo = 7 m/s	[h = 3.24 m, reaches]
b.	v_x = 14 m/s, v_yo = 8 m/s	[h = 4.08 m, misses]