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What is the maximum height achieved by the stone when it is thrown vertically upwards if it reaches that height in $4$ seconds? Take $g = 10 m / s^{2}$ .

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80 m

90 m

60 m

70 m

answer is A.

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Detailed Solution

The maximum height achieved by the stone is

80 m

.
Given, time taken by the stone for achieving maximum height,

t = 4 s

Gravitational acceleration

g = - 10 m / s^{2}

Here negative sign shows that the velocity of stone is decreasing
Let initial velocity and final velocity of the stone as

u

and

v

respectively
Final velocity

v = 0 m / s

(as the stone stopped at the maximum height)
We know, first equation of motion,

v = u + at

\Rightarrow u = v - at

⇒

u = v - gt

⇒

u = 0 - (- 10) (4)

\Rightarrow u = 40 m / s

Hence, the initial velocity of the stone is

40 m / s

.
Now from third equation of motion,

v^{2} - u^{2} = 2 as

⇒

v^{2} - u^{2} = 2 gh

⇒

{(0)}^{2} - {(40)}^{2} = 2 \times (- 10) \times h

⇒

h = - \frac{1600}{- 20}

⇒

h = 80 m

Therefore, the maximum height achieved by the stone is

80 m

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