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Question

A stone is thrown vertically upwards from the top of a tower 64 metres high according to the law S=48t-16t2. The greatest height attained by the stone above the ground is


A

36m

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B

32m

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C

100m

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D

64m

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Solution

The correct option is C

100m


Step1: Given data.

Height of the tower, h=64m

Equation of motion of the stone moving vertically upward, S=48t-16t2

Step2: Finding the greatest height attained by the stone above the ground.

We have,

S=48t-16t2 .…..i

On differentiating equation i both side we get,

dSdt=d48t-16t2dt

dSdt=48-32t ……ii

Where dSdt is the velocity of the stone.

Since, we know that on moving vertically upward the velocity of the stone at the highest point is zero.

Therefore,

dSdt=0

48-32t=0

t=1.5s

Now,

Substitute the value of t=1.5s in equation i we get,

S=48×1.5-16×1.52

S=36m

The total height attained by the stone above the ground=64+36=100m

Hence, option C is correct.


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