Challenging Projectile Motion Problems

If $$h(t) = -16t^2 + 16t + 480$$ , what is the initial height from which Jason jumped?

Given $$h(t) = -16t^2 + 16t + 480$$ , calculate the time when Jason reaches his maximum height.

If the height function is $$h(t) = -16t^2 + 32t + 100$$ , what is the initial velocity?

A ball is thrown upward from a $$50$$ ft cliff with an initial velocity of $$20$$ ft/s. Its height is given by $$h(t) = -16t^2 + 20t + 50$$ . How long does it take to reach the maximum height?

A rock is thrown upward from the ground with an initial velocity of $$24$$ ft/s. Its height is modeled by $$h(t) = -16t^2 + 24t$$ . How high does the rock go before it starts falling back down?

A diver jumps from a platform $$32$$ feet above the water with an initial velocity of $$8$$ ft/s upward. The height is given by $$h(t) = -16t^2 + 8t + 32$$ . How long is the diver in the air before hitting the water? (Round to the nearest tenth)

A ball is thrown upward from a $$10$$ ft platform with an initial velocity of $$40$$ ft/s. Its height is $$h(t) = -16t^2 + 40t + 10$$ . At what time will the ball be $$42$$ feet above the ground? (Round to the nearest tenth)

A basketball is shot upward from $$6$$ feet above the ground with an initial velocity of $$18$$ ft/s. Its height is $$h(t) = -16t^2 + 18t + 6$$ . How long does it take for the ball to reach the ground? (Round to the nearest tenth)

A stone is thrown upward from a $$20$$ ft ledge with an initial velocity of $$12$$ ft/s. Its height is $$h(t) = -16t^2 + 12t + 20$$ . What is the maximum height reached by the stone?

A ball is thrown upward from the ground with an initial velocity of $$32$$ ft/s. Its height is $$h(t) = -16t^2 + 32t$$ . How long does it take for the ball to return to the ground?