Mixed Two-Dimensional Projectiles

Practice Problems
Mixed Two-Dimensional Projectiles

Directions: This worksheet allows you to practice three different modes of releasing two-dimensional projectiles.

release A has s_y = 0
release B has s_y > 0
release C has s_y < 0
release D is thrown horizontally and has s_y < 0

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Question 1 For each of the following questions:

the release velocity V = 24 m/sec
when thrown at an angle (projectiles A, B, and C), the angle is 32º
the height of the cliff (projectiles C and D) is 18 meters
the barrier projectile B strikes is 3.6 meters tall

What is the height of the apex for projectile A?

21.1 meters8.3 meters29.4 meters

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Question 2 How fast is projectile A moving as it passes through its apex?

24.0 m/sec0 m/sec20.4 m/sec12.7 m/sec

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Question 3 What is the magnitude of projectile A's resultant impact velocity when it returns to the ground?

20.4 m/sec0 m/sec12.7 m/sec24 m/sec

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Question 4 How much time does projectile B spend in the air before it strikes the barrier?

2.27 sec0.32 sec1.30 sec2.85 sec

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Question 5 At what angle does projectile B strike the barrier?

25.1º32.0º64.9º22.5º

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Question 6 How far horizontally from the point of release is the barrier located?

26.4 meters46.2 meters28.9 meters

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Question 7 How high is the apex of projectile C above the bottom of the cliff?

47.4 meters39.1 meters30.7 meters26.3 meters

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Question 8 As projectile C passes through its apex which of the following statenments is true?

its instantaneous velocity equals zero, and its acceleration equals 0 //sec²its instantaneous velocity equals 20.4 m/sec and its acceleration is -9.8 m/sec²its instantaneous velocity equals 22.7 m/sec and its acceleration is +9.8 m/sec²its instantaneous velocity equals 24.0 m/sec and its acceleration is -9.8 m/sec²

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Question 9 What is the magnitude of projectile C's resultant impact velocity when it returns to the ground?

30.5 m/sec24.0 m/sec22.7 m/sec

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Question 10 How much time does projectile C spend in the air before it strikes the ground at the base of the cliff?

1.02 seconds3.61 seconds0.75 seconds2.68 seconds

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Question 11 How much time does projectile D spend in the air before it strikes the ground at the base of the cliff?

2.60 seconds1.92 seconds5.56 seconds

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Question 12 At what angle does projectile D strike the ground at the base of the cliff?

48.1º38.2º38.0º41.9º

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Question 13 How far from the base of the cliff does projectile D strike the ground?

39.0 meters133.4 meters46.0 meters