Question

The goal is to shoot down my friends drone with a paintball. We need to know how quickly my paintball will reach a maximum altitude. And we need to know if my paintball will even reach the height required to reach the drone. His drones maximum altitude is 1200 ft.

A paintball will be shot directly upward with an initial velocity of 293 feet per second (approximately 200 mph) from an initial height of 7 ft. The height of the paintball (in feet) after t seconds if given by formula h(t)=-16t2+293t+7. After how many second will the ball reach its maximum height? What is that maximum height?

How many seconds will the Paintball take to reach maximum altitude. (Round to the nearest whole number)

What is the maximum altitude of the paintball? (Round to the nearest whole number)

Thanks!

Answer 1

So we need the vertex of the parabola
h(t) = -16t^2 + 293t + 7
the t of the vertex is -b/(2a) = -293/-32 = 293/32 seconds or in 9.15625 seconds

plug that into h(t)
= ...
= appr 1348.4 ft

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