Question

Kyle, a 95.0 kg football player, leaps straight up into the air (with no horizontal velocity) to catch a pass. He catches the 0.430 kg ball precisely at the peak of his jump, when he is 0.538 meters off the ground. He hits the ground 0.0307 meters away from where he leapt. If the ball was moving horizontally when it was caught, how fast was the ball traveling?_____m/s

Answer 1

The velocity of ball is 20.63 m/s.

Step-by-step explanation:

Given that,

Mass of football player = 95.0 kg

Mass of ball = 0.430 kg

Distance = 0.538

We need to calculate the time

Using equation of motion

`s = ut+(1)/(2)gt^2`

`0.538=0+(1)/(2)*9.8* t^2`

`t^2=(2*0.538)/(9.8)`

`t=\sqrt{(2*0.538)/(9.8)}`

`t=0.33\ sec`

We need to calculate the velocity

Using formula of velocity

`s=v* t`

`v=(s)/(t)`

Put the value into the formula

`v=(0.0307)/(0.33)`

`v=0.093\ m/s`

We need to calculate the velocity of ball

Using conservation of momentum

`m_(1)v_(1)+m_(2)v_(2)=mv`

Put the value into the formula

`95.0*0.093+0.430*0.093=0.430* v`

`v=(8.87499)/(0.430)`

`v=20.63\ m/s`

Hence, The velocity of ball is 20.63 m/s.