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A stone is dropped from a tower with no initial velocity. It is observed that it strikes the ground after $5$ seconds. Which of the following would be the height of the tower?

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122.5 m

1225 m

12.25 m

1.225 m

answer is A.

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Detailed Solution

Initial velocity of first stone

u = 0 m s^{- 1}

Time taken for the stone to reach the ground

t = 5 s

Acceleration due to gravity

g = 9.8 m s^{- 2}

We are asked to find the final height of the tower.So we need to find the total distance

S

traveled by the stone.
With the given data we can use the equation

S = ut + \frac{1}{2} a t^{2}

Here

a = g

Here we can write the above equation as

S = ut + \frac{1}{2} g t^{2} - - - - (i)

Substituting all the values in the equation (i)
We get

S = 0 \times 5 + \frac{1}{2} \times 9.8 {\times (5)}^{2}

= > S = 0 + \frac{245}{2}

= > S = 122.5 m

Thus the height of the tower is

122.5 m

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