If a table tennis champion Bounce is a ping-pong ball up and down between his pattern for1 m away if it takes .75 seconds for the ball to reach the floor what is the initial velocity of the ball

The initial velocity of the ball is : 2.34 m/s

Explanation:

Taking this case as a free fall where the ball falls a distance of 1 m in 0.75 seconds to reach the floor, the initial velocity is calculated as;

d= v₁*t + 0.5*a*t² kinematic equation for displacement d where v₁ is the initial velocity, a is acceleration due to gravity and t is time.

Given in the question;

d= - 1 m negative sign means the displacement is downwards

a= - 9.8 m/s² for a free-falling

t= 0.75 sseconds for the ball to reach the floor

v₁ = initial velocity of the ball in m/s

Substitute real values in the formula as;

d= v₁*t + 0.5*a*t²

-1= v₁*0.75 + 0.5 * -9.8 *0.75²

-1=0.75v₁ -2.76 solve for v₁ as;

-1+2.76 = 0.75 v₁

1.76 = 0.75 v₁

1.76/0.75 = 0.75 v₁/0.75

2.34 = v₁

The initial velocity of the ball is : 2.34 m/s