Question

Neglecting air​ resistance, the distance s(t) in feet traveled by a freely falling object is given by the function s(t) = 16 t²​, where t is time in seconds. The height of a certain tower is 949 feet. How long would it take an object to fall to the ground from the top of the​ building?

Answer 1

7.7 seconds

Explanation:

To find how long would take to the object fall to the ground from the top of the building, we just need to use the function given (which express the position of the object in a certain time):

s(t) = 16*t2

The height of the tower is 949 feet, so the total height the object will fall is 949 feet. Using this value for s(t), we can find the value of t (the total amount of time that will take to travel this distance):

949 = 16*t2

t2 = 949 / 16

t2 = 59.3125

t = 7.7015 seconds

So it would take 7.7 seconds for the object to fall to the ground from the top of the building.