A ball is thrown straight upwards with an initial velocity of 30 m/s from a height of 1 meter on the ground. The height of the ball as a function of time measured in seconds after it is thrown is given by s(t) = 1 + 30t − 4.9t^2

a) What is the velocity function v(t) showing the velocity of the ball at time t?
b) What is the velocity of the ball after 2 seconds?

c) When does the ball reach its maximum height?

d) If the person who threw the ball catches it when it gets back to their hand height of 1 meter, how long does the ball stay in the air?

e) What is the speed of the ball when it gets back to the thrower’s hand?