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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 I : 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-g t_(AB)`
`therefore 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 of descent then
`70=(1)/(2)(10)t_(BC)^(2)`
`therefore t_(BC)=sqrt(14)=3.7s`
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