Question

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second then its height H after T seconds is given by the equation h(t)=-16t^2+128t (if air resistance is neglected). When will the object reach its maximum height?

A. 8 seconds
B. 6 seconds
C. 0 seconds
D. 4 seconds​

Answer 1

The toy rocket will reach its maximum height after 4 seconds.

Step-by-step explanation:

The maximum height of the toy rocket can be found by determining when the vertical velocity equals zero. In the equation h(t)=-16t^2+128t, the maximum height occurs at the vertex of the parabolic equation. The time to reach the maximum height can be found using the formula t = -b/2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = -16 and b = 128. Plugging in these values, we get t = -128/2(-16) = 4 seconds. Therefore, the object will reach its maximum height after 4 seconds. The correct answer is D: 4 seconds.

Answer 2

4 seconds

Step-by-step explanation: