Question

The height ,H, in feet , of an object dropped from the top of a building after t seconds is given by the function H(t) =-64t2+169. Determine algebraically how many seconds it will take for the object to reach the ground

Answer 1

Therefore it will take
`\frac{13}8` s for the object to reach the ground.

Explanation:

Given function is

H(t) = -64 t²+169.

where H is height in feet, and t is time in second.

When the object touches the ground, the height of the object will be zero.

i.e H(t) = 0.

Therefore

H(t) = 0

⇒ -64 t²+169=0

⇒ -64 t²= -169

`\Rightarrow t^2= (-169)/(-64)`

`\Rightarrow t^2= (169)/(64)`

`\Rightarrow t=\pm \sqrt{(169)/(64)}` [ square root both sides]

`\Rightarrow t=\pm(13)/(8)`

Time can not be negative.

Therefore
`t=(13)/(8) \ s`

Therefore it will take
`\frac{13}8` s for the object to reach the ground.