Problem 1

A small ball is launched from the edge of a cliff of height

h=20

m with initial speed

v_0=20

m/s at

30^\circ

above the horizontal. Neglect air resistance and take

g=10

m/s

^2

. Set the origin at the foot of the cliff, with

x

horizontal in the launch direction and

y

upward; the ground is

y=0

. (a) Find the time from launch until impact. (b) Find the horizontal coordinate and both velocity components at impact. (c) Determine the maximum height above the ground and when it is reached.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

0=20+10t_f-5t_f^2,\quad t_f=1+\sqrt5\simeq3.236\ \mathrm{s}

problems.proof.analysis

Set the vertical coordinate to zero at the ground. The roots are $1\pm\sqrt5$ ; the negative root is before launch, so only the positive root is physical.

problems.proof.pitfall. Do not treat this as a horizontal launch from a 20 m drop: the initial vertical velocity is

10

m/s upward.