Question II

II) A movie stuntman is to run across a rooftop and jump horizontally off it, to land on the roof of the next building (see Figure below). Before he attempts the jump, he wisely asks you to determine whether it is possible. Can he make the jump if his maximum rooftop speed is 4.5 m/s? Explain. An answer with just YES or NO will not be acceptable.

Solution:
Let's find the time that it takes our stuntman to fall 4.8m in the $\hat{y}$ direction with an initial y velocity of zero.
$\Delta y = \frac{1}{2}gt^{2}$
$-4.8 m = \frac{1}{2}gt^{2}$
t = .989 sec when our stuntman has fallen to the height of the other building. Let's see how far he has gone in the $\hat{x}$ direction in that amount of time.
$\Delta x = v_{0} t$
$\Delta x = 4.45 m$
In other words, when our stuntman is at the height of the shorter building, then he is still 1.75 m away from making it to the rooftop. He will not make the jump. There were other ways to solve this problem, but all correct ones involved separating the motion into $\hat{x}$ and $\hat{y}$ components and finding or using the time of travel.