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

problems.proof.prevStep problems.proof.nextStep

x(t)=v_0t,\qquad y(t)=H-\frac12gt^2

problems.proof.analysis

There is no horizontal acceleration, so horizontal velocity stays constant. Vertically the initial velocity is zero and acceleration is downward with magnitude $g$ .