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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

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)`=70 m

Stage-iii : If `t_(BC)` is time of descent then
`70=1/2 (10)t_(BC)^2`
`therefore t_(BC)=sqrt14=3.7 s`
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