Answer to Question #79225 in Mechanics | Relativity for Hrutil Tandel

Question

A rocket is firing vertically from the ground.It moves upwords with a constant acceleration 10m/s^2 for 30 s after which the fuel is consumed.After what time from the instant of firing the rocket will attain the maximum height?(Take g =10m/s^2)

Answer 1

Let’s first find the velocity attained by the rocket in 30 s before the fuel is consumed:
v=v_0+at,
here, v is the velocity attained by the rocket in 30 s, v_0=0 is the initial velocity of the rocket, a is the acceleration of the rocket, t is time.
Then, we get:
v=v_0+at=0 m/s+10 m/s^2 ∙30 s=300 m/s.
Now, we can find the time taken to reach the maximum height after the fuel is consumed:
v=v_0-gt,
here, v=0 is the final velocity of the rocket at the maximum height, v_0=300 m⁄s is the initial velocity of the rocket, g=10 m⁄s^2 is the acceleration due to gravity, t is the time taken to reach the maximum height after the fuel is consumed.
Then, we get:
t=-(v-v_0)/g=-(0 m/s-300 m/s)/(10 m/s^2 )=30 s.
Finally, we can find the total time in which the rocket will attain the maximum height:
t_total=30 s+30 s=60 s.