Projectile Motion Challenge Problems

Projectile Motion Challenge Problems

1.  AP: Derive the range formula.

2.  An archer shoots an arrow from a cliff 20 meters high at an angle of 70 degrees above horizontal with an initial velocity of 70 m/s.

a.  How long is the arrow in the air?

b.  How far away from the base of the cliff does it land?

c.  What is the arrow’s final velocity when it hits the ground?

d.  At what height is the arrow pointed 10 degrees below horizontal?

e.  At what time(s) and height(s) is the arrow moving at half it’s original speed?

3.  A catapult is positioned at the edge of a 350 meter cliff. It launches with an initial velocity of 60 m/s at an angle of 50 degrees above the horizontal at a height of 5 meters above the ground. Below the cliff, Sparkles, the last living unicorn on Earth is 2000 meters away but moving toward the cliff at a constant velocity of 7 m/s.

a.  How long after initially spotting Sparkles should the catapult fire? (assuming they want to hit the unicorn)

b.  If Sparkles was accelerating at a rate of 0.40 m/s2 (including the initial velocity of 7 m/s), what is the new firing time?

4.  An anti-aircraft unit hears a report that an enemy plane was spotted 5000 meters away moving towards their position at a constant velocity of 115 m/s and at an altitude of 900 meters. The anti-aircraft shell will leave the gun at an angle of 60 degrees, 5 meters above the ground, with an initial velocity of 160 m/s.

How long after hearing the initial report should they fire the weapon in order to hit the plane? (“They should fire ______seconds after hearing the initial report”)

Assuming they miss on the first shot, when should they fire the second shot? (“They should fire the second shot ______seconds after hearing the initial report.”)

5.  AP: An anti-aircraft unit hears a report that an enemy plane was spotted some distance Dx away moving towards their position at a constant velocity of 115 m/s directed 15 degrees below horizontal and at an altitude of 900 meters. The anti-aircraft shell (which is fired immediately) will leave the gun at an angle of 60 degrees, 5 meters above the ground, with an initial velocity of 160 m/s and destroy the plane.

a.  How far away was the plane (Dx)?

b.  What was the (x,y) position of the plane 30 seconds before firing?