A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an initial speed of $5 \mathrm{~ms}^{-1}$. Neglecting the air resistance, the speed with which the stone hits the ground will be \_\_\_\_ $\mathrm{ms}^{-1}$ (given, $\mathrm{g}=10 \mathrm{~ms}^{-2}$).

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Kinematics

A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an initial speed of

5 ms^{- 1}

. Neglecting the air resistance, the speed with which the stone hits the ground will be ____

ms^{- 1}

(given,

g = 10 ms^{- 2}

(A)20
(B)15✓ Correct
(C)30
(D)25

Answer: (B)

Solution

The horizontal velocity stays constant throughout the flight,

v_{x} = 5 m s^{- 1}

. Falling the height

h = 10 m

builds a vertical velocity

v_{y} = 2 g h = 2 (10) (10) = 102 m s^{- 1}

. The speed at the ground is the resultant of the two,

v = v_{x}^{2} + v_{y}^{2} = 25 + 200 = 225 = 15 m s^{- 1} .

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Single correct option

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