Question

A particle is moving along a projectile path where the initial height is 160 feet with an initial speed of 144 feet per second. What is the maximum height of the particle?

Answer 1

128 feet
224 feet
272 feet
484 feet

Answer 2

Assuming Earth's gravity, the formula for the flight of the particle is:

s(t) = -16t^2 + vt + s = -16t^2 + 144t + 160.

This has a maximum when t = -b/(2a) = -144/[2(-16)] = -144/(-32) = 9/2.

Therefore, the maximum height is s(9/2) = -16(9/2)^2 + 144(9/2) + 160 = 484 feet.