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) = −

Question

Pavel [41]

2 years ago

7

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

Mathematics

2 answers:

riadik2000 [5.3K] · Answer 1 · 2022-09-17T22:40:51+03:00

riadik2000 [5.3K]2 years ago

8 0

Hello there.

<span>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</span>

hoa [83] · Answer 2 · 2022-09-17T20:58:33+03:00

To calculate the velocity, we use the given expression above which is <span>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.

</span>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