A rocket is fired upward from the earth's surface such that it cr… - Vidyadip

MCQ

A rocket is fired upward from the earth's surface such that it creates an acceleration of $19.6 \,m/sec^2$. If after $5 \,sec$ its engine is switched off, the maximum height of the rocket from earth's surface would be.........$m$

A
$245$
B
$490$
C
$980$
✓
$735$

✓

Answer

Correct option: D.

$735$

d
(d) Given $a = 19.6\;m/{s^2} = 2g$

Resultant velocity of the rocket after $5 \,sec$

$v = 2g \times 5 = 10g\;m/s$

Height achieved after 5 sec, ${h_1} = \frac{1}{2} \times 2g \times 25 = 245\,m$

On switching off the engine it goes up to height ${h_2}$ where its velocity becomes zero.

$0 = {(10g)^2} - 2g{h_2} \Rightarrow {h_2} = 490\,m$

$\therefore $Total height of rocket $ = 245 + 490 = 735\;m$

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