Question

A rocket is fired vertically up from the ground with a resultant vertical acceleration of 10m/s^2 . The fuel is finished in 1 minute and the rocket continues to move up. After how much time from then will the maximum height be reached? Give calculations

Answer 1

Answer:

1 min

Explanation:

Given,

• A rocket is fired vertically up from the ground with a resultant vertical acceleration of 10m/s^2 .
• The fuel is finished in 1 minute and the rocket continues to move up.

Solution,

Rocket is fired vertically upward with initial velocity u = 0, and Net Force = Upward Force - mg = ma, where a = + 10 m/s^2

Equation of motion for uniformly accelerated body:

v = u + at ; where u = 0, a = +10 m/s^2, t = 60s

v = 0 + 600 m/s

At the time the fuel gets exhausted, the velocity of the rocket would be +600 m/s (upward). At this moment, this can be considered as vertical projection with initial velocity u = 600m/s, v = 0 (at maximum height), a = -10 m/s^2 (approx)

v = u + at

0 = 600 - 10t

t = 600/10

t = 60s = 1 min

Hence, It'll take 1 more min to reach the maximum height.