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Q.

A projectile is thrown from the top of a tower. It takes $4$ seconds to hit the ground. If acceleration due to gravity is $10 m s^{- 2}$ . Which of the following is the height of the tower?

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a

80 m

b

800 m

c

8 m

d

0.8 m

answer is A.

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Detailed Solution

The height of the tower is

80 m

.
Time taken for the projectile to reach the ground

t = 4 s

Acceleration due to gravity

g = 10 m s^{- 2}

(given)
We are asked to find the height of the tower. Once it starts its horizontal motion, the velocity turns zero at a particular distance of its horizontal direction. Once the velocity becomes zero the projectile will start falling down under the influence of gravity. So we can consider that the vertical motion of the projectile starts with initial velocity zero and the vertical distance traveled by the projectile in

4

seconds would be the height of the tower.
Initial velocity of the projectile

u = 0 m s^{- 1}

We know that

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

Where

S

is the distance traveled

a

is the acceleration
Here

a = g

So 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 4 + \frac{1}{2} \times 10 {\times (4)}^{2}

\Rightarrow S = 0 + \frac{160}{2}

\Rightarrow S = 80 m

Thus, the vertical distance traveled by the projectile in

2

seconds is

80 m

. So we can conclude that the height of the tower is

80 m

.

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A projectile is thrown from the top of a tower. It takes 4 seconds to hit the ground. If acceleration due to gravity is 10 ms-2. Which of the following is the height of the tower?