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A rocket is fired vertically upwards wit...

A rocket is fired vertically upwards with a net acceleration of `4 m//s^2` and initial velocity zero. After `5s` its fuel is finished and it decelerates with g. At the highest point its velocity becomes zero. Then, it accelerates downwards with acceleration g and return back to ground. Plot velocity-time and displacement -time graphs for the complete journey. Take `g=10m//s^2.`

Text Solution

Verified by Experts

The correct Answer is:
A
In the graphs,
`v_a=at_(OA)=(4)(5)=20 m//s`
`v_B=0=v_A-g t_(AB)`
`:. t_(AB)=v_A/g=20/10=2s`
`:. t_(OAB)=(5+2)s=7s`
Now, `s_(OAB)`=area under v-t grpah between 0 to 7s
`=1/2(7)(20)=70m`

Further, `|s_(OAB)|=|s_(BC)|=1/2g t_(BC)^2`
`:. 70=1/2(10) t_(BC)^2`
`:. t_(BC)=sqrt14=3.7s`
`:. t_(OABC)=7+3.7=10.7s`
Also, `s_(OA)` = area under v-t graph between OA
`=1/2(5)(20)=50m`
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Knowledge Check

  • A rocket is fired vertically upwards and moves with net acceleration of 10 m//s^(2) . After 1 min the fuel is exhausted. The time taken by it to reach the highest point after the fuel is exhausted will be:

    A
    10 sec
    B
    20 sec
    C
    30 sec
    D
    60 sec

  • If a ball is thrown vertically upwards with a velocity of 40m//s , then velocity of the ball after 2s will be (g = 10m//s^(2))

    A
    `15m//s`
    B
    `20 m//s`
    C
    `25m//s`
    D
    `28 m//s`

  • In a linear S.H.M., the acceleration of the particle is zero, when its velocity is

    A
    Zero
    B
    Maximum
    C
    Half of its maximum value
    D
    Minimum