To test the quality of a tennis ball, you drop it onto the floor from a height of 4.31 m. It rebounds to a height of 2.51 m. If the ball is in contact with the floor for 12.6 ms, what is its average acceleration during that contact?
mgh₁ = mv₁²/2
v₁=sqrt(2gh₁) = sqrt(2•9.8•4.31)=9.2 m/s
mv₂²/2= mgh₂
v₂ =sqrt(2gh₂) = sqrt(2•9.8•2.51)=7 m/s
a=[v(fin) – v(in)]/t
v(fin) =v₂ (directed upward )
v(in)] = v₁ (directed downward )
a= {v₂ - (-v₁)}/t ={v₂ +v₁)}/t=
=(9.2+7)/12.6•10⁻³=1285 m/s² (directed upward)
To find the average acceleration of the tennis ball during its contact with the floor, we can use the equation for average acceleration:
Average acceleration = (change in velocity) / (time taken)
In this case, the change in velocity can be calculated by subtracting the initial velocity from the final velocity. The initial velocity of the ball can be determined by calculating its velocity just before hitting the floor, and the final velocity can be determined by calculating its velocity just after leaving the floor.
To find the initial velocity, we can use the equation for the velocity of an object in free fall:
v = sqrt(2gh)
Where:
v = velocity
g = acceleration due to gravity (9.8 m/s²)
h = height
Plugging in the values:
v_initial = sqrt(2 * 9.8 m/s² * 4.31 m)
Once we have the initial velocity, we can calculate the final velocity using the equation for the velocity of an object after free fall:
v_final = sqrt(v_initial^2 + 2gh)
Plugging in the values, we have:
v_final = sqrt((initial velocity)^2 + 2 * 9.8 m/s² * 2.51 m)
Now that we have the initial and final velocities, we can calculate the change in velocity by subtracting the initial velocity from the final velocity:
Change in velocity = v_final - v_initial
Lastly, we can find the average acceleration by dividing the change in velocity by the time taken:
Average acceleration = (Change in velocity) / (Time taken)
Plugging in the values, we can now calculate the average acceleration.