How fast was the ball traveling when it hit the ground?

Question

For a building having a height equal to the quantity you have recorded for Day in meters (in our example 15 meters), compute the time required for the ball to fall to the ground while experiencing acceleration due to gravity (g=9.8m/s2). The meter is 4.

h=4m

How fast was the ball traveling when it hit the ground?

Answer 1

A derivation of the equation of motion is”

v = u + a∆t

Where, v is the final velocity

           u, is the initial velocity

           a, is the acceleration due to gravity

           and ∆t is the time elapsed.

u, initial velocity is zero

a, is 9.8 m/sec^2

Solving for Δt

Δt = (u -v)/a

Δt = ( v - (0))/a = v/a

To get v, use another equation of motion,

v² = u² +2a∆x

v² = 0 + (2)(9.8m/sec²)(4 m) = 78.4 m²/sec²

v = 8.85 m/sec

now knowing v, you can plug it in to get ∆t

∆t = v/a

∆t = (8.85 m/sec)/(9.8/sec²)

∆t = 0.9.03 sec