Question

solve the equation. round to the nearest tenth, if necessary.
if an object is propelled upward from a height of 32 feet at an initial velocity of 64 feet per second, then its height after t seconds is given by the equation h = -16t² + 64t + 32, where h is in feet. after how many seconds will the object reach a height of 96 feet?
a 4 sec
b 2 sec
c 1 sec
d 8 sec

Explanation:

Step1: Substitute \(h = 96\) into the equation

We have the equation \(h=-16t^{2}+64t + 32\). Substituting \(h = 96\) gives \(96=-16t^{2}+64t + 32\).

Step2: Rearrange the equation

Subtract 96 from both sides: \(0=-16t^{2}+64t + 32 - 96\), which simplifies to \(0=-16t^{2}+64t - 64\). Divide through by -16: \(t^{2}-4t + 4 = 0\).

Step3: Factor the quadratic equation

The quadratic \(t^{2}-4t + 4=(t - 2)(t - 2)=0\).

Answer:

B. 2 sec