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menco
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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