Kinematics Reasonings

# A body is thrown vertically upwards with a velocity ‘u’. What is the velocity at half the greatest height it can reach?

Let $h$ be the greatest height reached by the body when thrown upwards with a velocity $u$. At maximum height, the velocity will be zero $(v=0).$

$\therefore v^2=u^2-2gh$ $0=u^2-2gh$ $\therefore h=\frac{u^2}{2g}$

At half the greatest height, the distance travelled by the body is $\frac{h}{2}$. Let $v’$ be the velocity at this point. $\therefore v’^2=u^2-2g\frac{h}{2}$ $v’^2=u^2-2g×\frac{u^2}{4g}$ $v’^2=u^2-\frac{u^2}{2}$ $v’^2=\frac{u^2}{2}$ $\therefore v’=\frac{u}{\sqrt{2}}$

Thus, the velocity at half the greatest height will be $\frac{1}{\sqrt{2}}$ times the velocity with which it was thrown upwards.

[Equations used above are deduced from Motion Under Gravity]

#### SIMILAR QUESTIONS

A body thrown vertically upwards takes ‘t’ time to reach the highest point. What would be the time required to reach the same point during its return?

A body reaches a certain height when thrown with a certain velocity. What is the height reached if the velocity is doubled?

A body is dropped from a certain point and it travels a height ‘h’ after some time. What would be the time required to travel double the height?

Rain drops hitting the side windows of a car in motion often leave diagonal streaks. Why?

If a body is thrown vertically upward from a vehicle moving with uniform velocity, where will the body fall?

A body is dropped from a certain point and it reaches a velocity ‘v’ after some time. What would be the velocity reached after twice the time?