Question

A body is thrown upwards with velocity ‘u ’ and it attains a height h. Write the equation of motion for the body.

Answer 1

Explanation:

Since a body is thrown upwards with velocity ‘u ’ and it attains a height h.

So,the equation of motion for the body.

Assume initial velocity to be zero and final velocity is u.

Apply first equation of motion,

$u = 0 - gt = -gt$  Here a = -g.

Apply second equation of motion,

$u^{2} -0^{2}  =-2gh$

$u^{2} =-2gh$

Apply third equation of motion,

$h =0 + \dfrac{-gt^{2}}{2} =\dfrac{-gt^{2} }{2}$

Answer 2

Explanation:

Let u is the velocity of the body with which it was thrown upwards. It attains a height of h. We need to write the equation of motion for the body.

When it attains its height, its final speed is equal to 0. It will move under the action of gravity. The first equation of motion is given by :

$v=u+at$

v = 0 and a = -g

$u=-gt$

The second equation of motion is given by :

$h=ut+\dfrac{1}{2}(-g)t^2\\\\h=-\dfrac{1}{2}gt^2$

The third equation of motion is given by :

$v^2-u^2=-2gh\\\\u^2=2gh$

Hence, this is the required solution.

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Kinematics

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