Two hikers, Alisha and Caleb, are resting on a hillside; the hill has a slope of 30 degrees,
and Caleb is sitting above Alisha, eight meters away. They’ve brought fruit to eat on the
trail, but they want to trade.
a) Caleb throws an orange down to Alisha, with its initial velocity directed horizontally.
How hard must he throw it for her to catch it?
b) She in turn throws an apple up to him, with its initial velocity directed at an angle 60
degrees above the horizontal (and thus 30 degrees above the slope). How hard must she
throw it for him to catch it?
The two components of the distance between them is
x = 4√3
y = 4
(a) if the velocity is v, then the two components are (using g=10 for simplicity)
x(t) = vt
y(t) = -5t^2
so, for the apple to travel 4√3 meters out, it will take 4√3/v seconds. It must fall 4 meters, so
5(4√3/v)^2 = 4
25(48/v^2) = 4
v= 5/√12 m/s
Do the same for part (b), but v will have both x- and y-components.