Problem 1

A ball is launched horizontally from a cliff of height

h=45\,\mathrm m

with initial speed

u=10\,\mathrm{m\,s^{-1}}

. Neglect air resistance and take

g=10\,\mathrm{m\,s^{-2}}

. Choose the launch point as the origin, with the horizontal axis forward and the vertical axis upward. The ground is a vertical distance

h

below the launch point; treat the ball as a point particle that hits no other object before landing. Measure time from the instant it leaves the cliff. (a) Find the time to reach the ground and the horizontal range. (b) Determine the velocity components just before impact. (c) Find the impact speed and its angle below the horizontal.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

v=\sqrt{v_x^2+v_y^2}=31.6\,\mathrm{m\,s^{-1}}

problems.proof.analysis

The impact speed is the magnitude of the perpendicular velocity components, found by the Pythagorean theorem.