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

t_{\max}=v_{0y}/g=1.00\ \mathrm{s},\quad y_{\max}=20+10(1)-5(1)^2=25.0\ \mathrm{m}

problems.proof.analysis

At the apex the vertical velocity vanishes, giving $t_{\max}=v_{0y}/g$ . Substitution into $y(t)$ gives 25 m; the collected results are $t_f=3.236$ s, $x_f=56.1$ m, $(v_x,v_y)=(17.3,-22.4)$ m/s, and $y_{\max}=25.0$ m.