Question

Jivesh brought his Model B rocket on a camping trip near the top of a mountain. He wants to model how it descends down the mountain. Here, he uses the equation h = −640t^2. When has the rocket descended 1,690 centimeters? Round your answers to the nearest hundredth. After t ≈ seconds, the rocket will have descended a distance of 1,690 centimeters. The negative time (can, cannot) be used in this context.

Answer 1

i. 1.63 s

ii. The negative time cannot be used in this context

Explanation:

i. Since h = −640t² and the rocket descends 1,690 m, h = -1,690 m (since there is a drop in height).

So, h = -640t²

t² = h/-640

t = √(- h/640)

Substituting h into the equation, we have

t = √(- h/640)

t = √[-(-1,690)/640]

t = √2.640625

t = 1.625

t ≈ 1.63 s

ii. So, the negative time cannot be used in this context because, the height drop is negative.