Chapter 2 Problem 66

Problem

A rock is thrown vertically upward with a speed of 12.0 m/s. Exactly 1.00 s later, a ball is thrown up vertically along the same path with a speed of 18.0 m/s.

(a) At what time will they strike each other?

(b) At what height will the collision occur?

(c) Answer (a) and (b) assuming that the order is reversed: the ball is thrown 1.00 s before the rock.

Solution

(a)

Choose up to be the positive direction. Let the throwing height of both objects be the $y$ = 0 location, and so $y_{0}$ = 0 for both objects. The acceleration of both objects is $a=g$.

The equation of motion for the rock:

$y_{\textrm {rock}}=y_{0}+v_{0{\textrm {rock}}}t+{\frac {1}{2}}at^{2}=v_{0{\textrm {rock}}}t+{\frac {1}{2}}gt^{2}$,

where $t$ is the time elapsed from the throwing of the rock. 

The equation of motion for the ball, being thrown 1.00 s later, is

$y_{\textrm {ball}}=y_{0}+v_{0{\textrm {ball}}}(t-1.00{\textrm {s}})+{\frac {1}{2}}a(t-1.00{\textrm {s}})^{2}=v_{0{\textrm {ball}}}(t-1.00{\textrm {s}})+{\frac {1}{2}}g(t-1.00{\textrm {s}})^{2}$