The change in velocity of the ball as it strikes the bat is 35 m/s - 20 m/s = 15 m/s. The impulse (the change in momentum) experienced by the ball as it strikes the bat is equal to the product of its mass and the change in velocity, which is 0.1 kg * 15 m/s = 1.5 kg m/s.
The average force experienced by the ball as it strikes the bat is equal to the impulse divided by the time of contact with the bat, which is 1.5 kg m/s / t = 500 N. Solving for t, we find that t = 1.5 kg m/s / 500 N = 0.003 s. This is the time the ball and bat spend in contact.