Question

A rocket is launched with an initial velocity of 1,000 ft/sec. Using the equation H = 1,000t - 16t^2, where H is the height of the rocket in feet and t is the time in seconds after launch, when will the rocket return to the ground?

A. 62.5 seconds
B. 125 seconds
C. 250 seconds
D. 500 seconds

Answer 1

To find when the rocket returns to the ground using the equation H = 1,000t - 16t^2, we set H to zero and solve for t, which yields t = 62.5 seconds, corresponding to option A.

Step-by-step explanation:

To determine when the rocket will return to the ground, we set the height equation H = 1,000t - 16t^2 equal to zero and solve for the time t.

Since the equation is quadratic, we can solve for t by factoring or using the quadratic formula. Here, t represents the time in seconds it takes for the rocket to return to the ground.

Setting H to 0, we get:
0 = 1,000t - 16t^2
0 = t(1,000 - 16t)
From the factored form, we can see that t = 0 or t = 1,000/16.

We ignore t = 0 because that represents the time at launch. Therefore, the rocket will return to the ground at t = 62.5 seconds, which corresponds to the answer choice A.