Question

A soccer player kicks a soccer ball of mass 0.40 kg that is initially at rest. The player's foot is in contact with the ball for 2.2 multiplied by 10-3 s. The force of the kick is given by the following formula for 0 t 2.2 multiplied by 10-3 s, where t is in seconds. F(t) = [(7.4 multiplied by 106)t - (2.8 multiplied by 109)t2] N (a) Find the magnitude of the impulse imparted to the ball. Incorrect: Your answer is incorrect. N

Answer 1

I = 7.96Ns

Step-by-step explanation:

We need to integrate the expression f the force F, so:

`I = \int\limits^(2.2ms)_(0) {7.4*10^6*t - 2.8*10^9*t^2} \, dt`

Solving the integral:

`I(t)=7.4*10^6*t^2/2 - 2.8*10^9*t^3/3` Evaluating the expression:

I = 7.96Ns