Answer:
[tex]t = 4.52[/tex]
Step-by-step explanation:
Given
[tex]f(t) = 100-4.9t^2[/tex]
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:
[tex]0= 100-4.9t^2[/tex]
Collect like terms
[tex]4.9t^2 = 100[/tex]
Divide through by 4.9
[tex]t^2 = \frac{100}{4.9}[/tex]
[tex]t^2 = 20.4081632653[/tex]
Take positive square roots of both sides
[tex]t = \sqrt{20.4081632653}[/tex]
[tex]t = 4.51753951453[/tex]
[tex]t = 4.52[/tex]
Hence, the ball hits the ground after 4.52 seconds
