A block was thrown with some velocity so that it reached a height of 20 meters. Find the velocity with which it is thrown?

When a ball is thrown vertically upward with some velocity say V₁ which is considered as the initial velocity for the upward path.

After a certain time period t, the ball reaches a height beyond which it can't move upwards anymore and stops there i.e. its velocity becomes zero at that height.

The height where the velocity becomes zero is known as the maximum height H.

So, for this upward movement, the final velocity V₂ will be 0 because the ball has stopped at the end of this upward traversal.

Now, for the question we have,

Maximum Height, $H=20m$

Initial Velocity, $u=x$

Final Velocity, $v=0$

Acceleration due to gravity, $g=9.8m/s^2$

We know Newton's equations of motion-

${v}^{2}={u}^{2}-2gH$

${0}^{2}={x}^{2}-2\times 9.8\times 20$

$0={x}^{2}-2\times \frac{98}{10}\times 20$

$0={x}^{2}-2\times 98\times 2$

${x}^{2}=392$

$x=\sqrt{392}$

$x=19.79m/s$

Initial velocity $u=19.79m/s$

Hence, the velocity with which a block was thrown to reach a height of 20 meters is 19.79m/s.

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Updated on: 10-Oct-2022

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