find its velocity and height 5 seconds later.

Question

Falling-Body Problem Near the surface of the earth, the acceleration of a falling body due to gravity is 32 feet per second per second, provided that air resistance is neglected. If an object is thrown upward from and initial height of 3000 feet with a velocity of 25 feet per second, find its velocity and height 5 seconds later.

Velocity:______feet per second, and height:_____feet

Hint: it is possible to get a negative velocky. Negative velocity indicates the object is traveling downwards,

Answer 1

Let y(t) be the height as a function of time in seconds.

gravity=g=-32 ft/s²

Initial velocity, v₀ = 25 ft/s

Initial height, h₀= 3000 ft

y(t)=gt²/2 + v₀t + h₀

Velocity, v(t) = y'(t) = gt+v₀

Velocity: y'(5) = -32(5)+25 = -135 ft/s

Height: y(5) = -16(5)²+25(5)+3000 = 2725 ft