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# A body is thrown vertically up from the ground with a speed vinitial and it reaches maximum height h at time t=to. What is the height to which it would have risen at time t=to/2

A
0.75h
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B
h
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C
0.5h
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D
0.3h
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Solution

## The correct option is A 0.75hIn this problem we have free fall motiony(t)=yinitial+vinitialt−4.9t2v(t)=vinitial−9.8tv2(t)−v2initial=−19.6[y(t)−yinitial]The initial height of the object is 0 (ground level)∴y(t)=vinitialt−4.9t2→1v(t)=vinitial−9.8t→2v2(t)−v2initial=−19.6(t)→3Case I: The object reaches the maximum height h at t0. At the maximum height the velocity of the object is zero and y(t0)=hh=vinitialt0−4.9t20→40=vinitial−9.8t0→5v2initial=19.6hCase II: Height of the object at t=t02Substitute this time in equation 1 and 3y(t0/2)=vinitialt02=4.9t204→7v(t0/2)=vinitial−9.8t02→8v2(t0/2)−v2initial=−19.6y(t0/2)→9We know, vinitial=t09.8Substitute in equation 4 and 7h=9.8t20−4.9t20=4.9t20→10y(t0/2)=9.8t204=4.9t204=3.675t20→11From equation 10t20=h4.9Substitute this in equation 11y(t0/2)=3.675t20=3.675×h4.9=0.75h  Suggest Corrections  0      Similar questions
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