A paper clip is dropped from the top of a 144-ft tower, with an initial velocity of 16 ft/sec. Its position function is s (t) = - 16t^2 + 144. What is its velocity in ft/sec when it hits the ground?

-96 - 64 - 32 0

Hello there.

A paper clip is dropped from the top of a 144-ft tower, with an initial velocity of 16 ft/sec. Its position function is s (t) = - 16t^2 + 144. What is its velocity in ft/sec when it hits the ground?

-96 - 64 - 32 0

-96

To calculate the velocity, we use the given expression above which is s (t) = - 16t^2 + 144. First, we calculate the time it takes to reach the ground. Then, differentiate the expression and substitute time to the differentiated expression.

s (t) = - 16t^2 + 144

0 = - 16t^2 + 144

t = 3

s' (t) = v = - 32t

v = - 32 (3)

v = - 96

Note: negative sign signifies that the object is going down