Question

An object is dropped from a height of 100 meters. The function below models the relationship between t , the number of seconds after the object is dropped, and f(t) , the height of the object after it is dropped. f(t)=100−4.9t^2 Approximately how many seconds does it take for the object to hit the ground?

Answer 1

Answer:

$t = 4.52$

Step-by-step explanation:

Given

$f(t) = 100-4.9t^2$

Required

Time it hits the ground

When the object hits the ground, the height is 0.

In other words:

f(t) = 0

So, we have:

$0= 100-4.9t^2$

Collect like terms

$4.9t^2 = 100$

Divide through by 4.9

$t^2 = \frac{100}{4.9}$

$t^2 = 20.4081632653$

Take positive square roots of both sides

$t = \sqrt{20.4081632653}$

$t = 4.51753951453$

$t = 4.52$

Hence, the ball hits the ground after 4.52 seconds