A stone that is dropped freely from the rest traveled half the total height in the second. with what velocity will it strike the ground

Velocity is the directional speed as an indication of its rate of change in position observed from a particular frame of reference.
velocity formula is basically displacement divided by time.

What is displacement:

Here,

Stone is dropped freely from rest, so it's Initial velocity will be zero.

u = 0 m/s

displacement is equal to half of total height.

y = h/2

since Stone is dropped freely, a=g ( acceleration of gravity)

According to Newton's equation of motion:

y = u* t + 1/2 (at^2)

h/2 = 0 + 1/2 (gt^2)

h = g* t^2 -----1

now at t= t+1 , displacement y = h

h = u* t + ½ g (t + 1)²

h = ½ g (t + 1)² -----2

comparing both equations,

g* t^2 = ½ g (t + 1)²

2t² = (t + 1)²

2t² = t² + 2t + 1

t² − 2t = 1

t² − 2t + 1 = 2

(t − 1)² = 2

t − 1 = ±√2

t = 1 ± √2

Since t > 0, t = 1 + √2.

So t+1 = 2 + √2.

At that time, the speed is:

v = at + u

v = g (2 + √2) + 0

v = g (2 + √2)

If g = 9.8 m/s²,

v = 33.5 m/s.

The stone will strike the ground with velocity of 33.5 m/s.

Learn more about velocity here:

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