Question

The National Institute of Health is testing sensors which measure the energy felt by goalkeepers when blocking soccer balls coming at them and the velocity of soccer balls. One sensor measuring velocity is inside a 16 ounce soccer ball, which is kicked by a player at an initial velocity of 31 m/s. The ball bounces off the goalkeeper at a final velocity of 2.25 m/s. How much energy in Joules should the sensor say the goalkeeper absorbed, not accounting for wind and drag

Answer 1

E = 216.76 J

Step-by-step explanation:

The amount of energy absorbed by the goalkeeper will be equal to the difference between the initial and the final kinetic energy of the ball.

`Energy\ Absorbed = Initial\ Kinetic\ Energy - Final\ Kinetic\ Energy\\Energy\ Absorbed = E = (1)/(2)mv_(i)^2 - (1)/(2)mv_(f)^2\\E = (1)/(2)m(v_(i)^2 - v_(f)^2)\\`

where,

m = mass of ball = (16 ounce)(0.0283495 kg/1 ounce) = 0.4535 kg

vf = final velocity = 2.25 m/s

vi = initial velocity = 31 m/s

Therefore,

`E = (1)/(2)(0.4535\ kg)[(31\ m/s)^2 - (2.25\ m/s)^2]`

E = 216.76 J