A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 58.8 m/s^2. The acceleration period lasts for time 8.00 s until the fuel is exhausted. After that, the rocket is in free fall. Find the maximum height ymax reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 m/s^2.

Question

Physics

Savanna Gibson

11 November, 12:54

A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 58.8 m/s^2. The acceleration period lasts for time 8.00 s until the fuel is exhausted. After that, the rocket is in free fall. Find the maximum height ymax reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 m/s^2.

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Answers (1)

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Eliezer Hogan · Answer 1

The maximum height will be 7408.8 meters

Explanation:

final velocity = initial velocity + acceleration * time

final velocity = 0 m/s + 58.8 m/s^2 * 6 s

Final velocity = 352.8 m/s

final velocity ^2 = initial velocity ^2 + 2 * acceleration * displacement

(352.8) ^2 = (0) ^2 + 2*58.8 * displacement

Solving for displacement,

height = 1058.4 meters.

After this, the rocket is in free fall, we can use the same equation.

final velocity ^2 = initial velocity ^2 + 2 * acceleration*displacement

final velocity = 0

0^2 = 352.8^2 + 2 * (-9.8) * displacement

displacement = 6350.4 meters

the maximum height will be 7408.8 meters