
Directions: Grab your paper and pencil. Be sure to show your work. You will need your calculator. FORMULAS: Throw/Launch: Feet: h = 16t^{2} + v_{0}t + h_{0} Meters: h = 4.9t^{2} + v_{0}t + h_{0}
Drop: remove middle term, v_{0}t.
(h = height; t = time in seconds; v_{0} = initial (starting) velocity; h_{0} = initial (starting) height)
1. 
By flipping a switch, a crane can release its wrecking ball which will fall to the ground. How long will it take the wrecking ball to hit the ground, if it is hanging at 50 feet above the ground? (State answer to the nearest tenth of a second.)



2. 
A model rocket is launched vertically upward from ground level with an initial velocity of 39.2 meters per second. Its height, h, after t seconds, is modeled by the equation h = 4.9t^{2} + 39.2t. How long, in seconds, will it be before the rocket hits the ground?



3. 
Fireworks are fired vertically upward from a platform 10 feet above the ground and with an initial velocity of 96 feet per second. What is the highest possible point (in feet) for the fireworks to explode?



4. 
Alvin is waiting in his tree fort for his sister to pass by. From his hiding spot 12 feet above the ground, Alvin drops a water balloon on his sister. How long (in seconds) will it take the balloon to hit his sister's head, which is 3 feet above the ground?



5. 
At the end of a graduation ceremony, it is customary for the graduates to throw their mortar boards (hats) up into the air. Carolyn throws her hat into the air and it leaves her hand at 5 feet above the ground with an initial velocity of 32 feet per second. How long will it take before her hat lands on the floor?
(State answer to the nearest second.)



6. 
During an enthusiastic game of hacky sack, Eli kicks the hacky sack straight up into the air with an initial velocity of 100 feet per second. The sack leaves his foot at a height of 3 feet. How long will it take for the hacky sack to return to his foot at 3 feet above the ground? (State answer to the nearest tenth of a second.)



7. 
As Charlie moves to look down the fairway to see where his golf ball is traveling, he is about to get hit in the head by his ball. Instead of traveling down the fairway, his golf ball went vertically into the air at an initial velocity of 160 feet per second. If the top of Charlie's head is 6 feet off the ground, how long does he have before the ball hits him on the head? (Assume the ball is at ground level to start. State answer to the nearest second.)



8. 
As Garth looks around he sees that his archer is shooting arrows up into the air instead of aiming at the enemy. The archer shoots the arrows vertically upward from 1 meter above the ground as he kneels behind the wall. The arrows have an initial velocity of 40 meters per second. What is the maximum height reached by the arrows, in meters, to the nearest meter?



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