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Question

A rocket of height h meters is fired vertically upwards.Its velocity at time t seconds is (2t+3) meters.second.If the angle of elevation of the top of the rocket from a point on the ground after 1 second of firing is π/6 and after 3 seconds it is π/3 then the distance of the point from the rocket is :

A
143 meters
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B
73 meters
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C
23 meters
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D
cannot be found without the value of h
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Solution

The correct option is D 73 meters
dxdt=2t+3,dx=(2t+3)dtx=t2+3t+c
BC=12+3×1+c=4+cBD=32+3×3+c=18+c
h+4+cAP=tan30,h+18+cAP=tan60
14AP=tan60tan30=313=23
AP=73
272509_134839_ans.PNG

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