JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Kinematics

A ball is released from a height

h

. If

t_{1}

and

t_{2}

be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between

t_{1}

and

t_{2}

Answer: (D)

Solution

For the first half distance

\frac{h}{2}

, using

s = \frac{1}{2} g t^{2}

\frac{h}{2} = \frac{1}{2} g t_{1}^{2} ⟹ h = g t_{1}^{2}

For the total distance

h

h = \frac{1}{2} g (t_{1} + t_{2})^{2}

Dividing the first equation by the second:

\frac{1}{2} = \frac{t _{1}^{2}}{( t _{1} + t _{2} ) ^{2}}

Taking square root:

\frac{1}{2} = \frac{t _{1}}{t _{1} + t _{2}}

Cross-multiplying and simplifying:

t_{1} + t_{2} = 2 t_{1} ⟹ t_{2} = (2 - 1) t_{1}

Therefore, option (D) is correct.

JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Single correct option