Answer
a) $v_0 = 1.08v$
b) $t_1 = .93t$
Work Step by Step
a) We know that the horizontal distance they travel is the same. We also know the following equation:
$ R = \frac{v_0^2sin(2\theta)}{g}$
Thus, it follows:
$\frac{v_0^2sin(2(60))}{g}=\frac{v^2sin(2(45))}{g}$
$.866v_0^2 = v^2$
$v_0 = 1.08v$
b) We know the following equation:
$v=\frac{d}{t}$
We know that the distances are the same in both cases, so we find:
$v_0t_1=vt$
Using substitution from above, we find:
$t_1 = .93t$
