A baseball is thrown from a platform 10 meters above the origin (so its position in the xy-plane is a function of time t, with x(0) = 0 and y(0) = 10) in such a way that its horizontal and vertical velocity are both initially 5 meters per second. You may assume that the acceleration due to gravity is −10 meters per second squared in the y-direction, and 0 in the x-direction.

(a) Find an expression for the velocity of the ball in the y-direction as a function of time vy(t).

(b) Find an expression for the position of the ball in the y-direction, i. e. its height, as a function of time y(t).

(c) At what time t does the ball hit the ground?

(d) What is the x-coordinate of the ball at the moment it hits the ground