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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

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Stage 1 : To find velocity of rocket after 5 seconds `V_(A)=0+at_(OA) =(4)(5)=20ms^(-1)`
Stage II: To find further time of ascent after 5 seconds.
`0=20-gt_(AB)" "t_(AB)=(20)/(10)=2"seconds"`
Here, the total vertical displacement of stage (i) and stage (ii) is `="area of OAB"=1/2 (7) (20)=70m`

Stage -III: If `t_(BC)` is time taken of descent then `70=1/2 (10) t_(BC)^(2) `
`t_(BC)=sqrt(14)-3.7s`
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