To find the speed of the object when it hits the ground, we need to find the velocity at that moment. Velocity is the derivative of displacement with respect to time.
The displacement function s = -16t^2 + 144 is a quadratic equation, so we can differentiate it to find the velocity function.
Differentiating s with respect to t:
ds/dt = -32t
To find the velocity at the moment the object hits the ground, we need to find the value of t when s = 0 (since the object hits the ground when the displacement is 0).
Setting s = 0 in the displacement function:
-16t^2 + 144 = 0
16t^2 = 144
t^2 = 144/16
t^2 = 9
t = ±√9
t = ±3
We discard the negative value of t because time cannot be negative in this context.
At t = 3 seconds, the object hits the ground.
To find the velocity at t = 3 seconds, substitute this value of t into the velocity function:
v = ds/dt
v = -32(3)
v = -96 ft/s
The object's speed when it hits the ground is 96 ft/s.
The height of an object dropped from a 144-foot-tall building is given by the function s=−16t2+144 , where s is in feet and t is in seconds. Find the object’s speed when it hits the ground.
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