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

Answer:

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

Step-by-step 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

$\Rightarrow t^2= \frac{-169}{-64}$

$\Rightarrow t^2= \frac{169}{64}$

$\Rightarrow t=\pm \sqrt{\frac{169}{64}}$   [ square root both sides]

$\Rightarrow t=\pm\frac{13}{8}$

Time can not be negative.

Therefore $t=\frac{13}{8} \ s$

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