## Essential University Physics: Volume 1 (4th Edition)

a) $v_0 = 1.08v$ b) $t_1 = .93t$
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: $t_1 = .93t$