Question

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 .

Answer 1

The maximum height will be 7408.8 meters

Step-by-step 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