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## Homework Statement

A projectile is fired straight upward with a velosict of 400m/s. From physics, its distance above the ground after t seconds is: s(t) = -16t^2 + 400t

A Find the time and velocity at which the projectile hits the ground

B Find the maximum altitude achieved by the projectile

C Find the acceleration at any time t.

## Homework Equations

s(t) = -16t^2 + 400t

## The Attempt at a Solution

A The surface s(t) = 0

0 = -16t^2+400t

16t^2-400 = 0

16t(t-25) = 0

16t = 0 t-25 = 0

t = 0 t = 25

v(t) = s'(t) = -32t+400

v(25) = -32(25)+400

= -400

The projectile hits the ground after 25 seconds at a velocity of 400m/s

B s'(t) = v(t) = -32t+400

0 = -32t+400

32t = 400

t = 12.5

s(12.5) = -16(12.5)^2+400(12.5)

= 2500m

The projectile reaches a max altitude of 2500m

C a(t) = v'(t) = -32m/s^2

The acceleration at anytime is 32m/s^2