Question

A test rocket is launched vertically from ground level. The rocket engine provides constant upward acceleration during the burn phase. What is the maximum height the rocket will reach if it had risen 49 m and acquired a velocity of 30 m/s?

a. 122.5 m
b. 147.5 m
c. 172.5 m
d. 197.5 m

Answer 1

We may apply the equations of motion to find the rocket's maximum height. The rocket gains a velocity of 30 m/s and rises 49 m. The maximum height the rocket will reach is 45.92 m. So, none of the given options are correct.

Step-by-step explanation:

To determine the maximum height the rocket will reach, we can use the equations of motion. The rocket rises 49 m and acquires a velocity of 30 m/s.

We can use the equation v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.

Since the rocket is moving vertically upwards, the acceleration is equal to the acceleration due to gravity (9.8 m/s²) and the final velocity is 0. Plugging in the values, we get:

0 = (30)² + 2(-9.8)s

-900 = -19.6s

s = 900 / 19.6

s = 45.92 m

Therefore, the maximum height the rocket will reach is 45.92 m.

None of the given options are correct.