Ana kicks a stationary 0.2 kg soccer ball. The ball leaves her foot at a speed of 20 m/s. a. What impulse was delivered to the ball?
b. The ball experiences 40N of force during the kick. How long were the ball and
foot in contact?

a. 24 kg m/s

b.  3/5s

Explanation:

a.impulse is the change in momentum so at first the momentum is zero because the ball was at rest and the final momentum is 1.2kg*20m/s=24 kg m/s

so the impulse would be (24-0) kg m/s=24 kg m/s

b. so the impulse equation is impulse is force *delts time

so 24 kg m/s=40N*t

t=24 kg m/s /40N=3/5 s

the velocity you are looking for is made up of two parts: horizontally velocity, vh, and its vertical velocity, vv. the actual velocity of the ball will be these two parts added together, and because velocity is a vector then they will need to be added vectorially.  

neglecting air resistance etc etc.,  

the horizontal velocity component will be constant (because there is no accelerating force in the horizontal direction.  

vh = 8 ms-1  

the vertical velocity component has an accelerating force: 'g'.  

using v = u +at where a = g = 9.81 ms-2.  

the vertical component of velocity, vv = 0 + gt = vv =9.81 x 2  

vv = 19.62 ms-1 . the zero appears because the virtical component of velocity at time t=0 is zero. remember, the ball was thrown horizontally.  

how fast it will be moving (it actual path (being a parabola )) will be the vector sum of these two.  

adding vectorally gives: -  

v = sqr root (8^2 + 19.62^2) = sqr root(64+384.9) = 21.18 or 21.2 ms-1