A ball is thrown vertically, from a height h=24.7m, with velocity vi. It lands on the ground after a time interval t. Coordinate axes are

A ball is thrown vertically, from a height h=24.7m, with velocity vi. It lands on the ground after a time interval Δt. Coordinate axes are indicated in the figure. Assume that air resistance is negligible.

a. Enter an expression for Δy in terms of Δt, a, and the vertical component of the initial velocity, vi.

b. Calculate the time, Δt, in seconds, for the case where the ball starts from rest.

c. Return to the general case, vi≠0, and enter an expression for the vertical component of the final velocity, vf ,at the instant of impact with the ground, in terms of vi, a, and Δt.

d. Calculate the value, in meters per second, of vf for the case where the ball is initially at rest.
 

h y X