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

Question

A rocket is fired vertically up from the ground. It moves upwards with a constant acceleration 10 m / s 2 for 30 seconds after which the fuel is consumed. After what time (in sec) from the instant of firing, the rocket will attain the maximum height? Take g=10 m / s 2 (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Time taken to attain max. velocity is t V =0+ t ...(1) time taken to attain maximum height (V=0) t' 0= V -a t ' ; V = at =a t ' ; t = t ' Total time to attain maximum height T = t + t '=2 t =2 × 30 sec =60 sec.

Q. A rocket is fired vertically up from the ground. It moves upwards with a constant acceleration $10 m / s^{2}$ for $30$ seconds after which the fuel is consumed. After what time (in $sec$ ) from the instant of firing, the rocket will attain the maximum height? Take $g = 10 m / s^{2}$

Time taken to attain max. velocity is $t$
$V = 0 + t$ ...(1)
time taken to attain maximum height
$(V = 0) t^{'}$
$0 = V - a t^{'}; V = a t = a t^{'}; t = t^{'}$
Total time to attain maximum height
$T = t + t^{'} = 2 t = 2 \times 30 sec = 60 sec$ .

Q. A rocket is fired vertically up from the ground. It moves upwards with a constant acceleration 10m/s2 for 30 seconds after which the fuel is consumed. After what time (in sec) from the instant of firing, the rocket will attain the maximum height? Take g=10m/s2

Time taken to attain max. velocity is t V=0+t ...(1) time taken to attain maximum height (V=0)t′ 0=V−at′;V=at=at′;t=t′ Total time to attain maximum height T=t+t′=2t=2×30sec=60sec.

Q. A rocket is fired vertically up from the ground. It moves upwards with a constant acceleration $10 m / s^{2}$ for $30$ seconds after which the fuel is consumed. After what time (in $sec$ ) from the instant of firing, the rocket will attain the maximum height? Take $g = 10 m / s^{2}$

Time taken to attain max. velocity is $t$
$V = 0 + t$ ...(1)
time taken to attain maximum height
$(V = 0) t^{'}$
$0 = V - a t^{'}; V = a t = a t^{'}; t = t^{'}$
Total time to attain maximum height
$T = t + t^{'} = 2 t = 2 \times 30 sec = 60 sec$ .