Problem 1

A small object is launched horizontally from the edge of a cliff of height

H

above level ground with initial speed

v_0

. Set the origin at launch,

x

horizontal along the launch direction and

y

upward; neglect air resistance and use

g=9.8\,\mathrm{m/s^2}

. The ground is level and wide enough to catch it. (a) Find flight time and range

R

. (b) Find the velocity components and speed just before impact. (c) Determine the trajectory angle below the horizontal at impact.

problems.proof.stepOf

v_x=v_0,\qquad v_y(t_f)=-gt_f=-\sqrt{2gH}

problems.proof.analysis

The horizontal component remains constant. The vertical component grows linearly with time and is negative because it points downward.