A 103 kg physics professor has fallen into the Grand Canyon. Luckily, he managed to grab a branch and is now hanging 93 m below
the rim. A student (majoring in lin- guistics and physics) decides to perform a rescue/experiment using a nearby horse. After lowering a rope to her fallen hero and attaching the other end to the horse, the student measures how long it takes for the horse to pull the fallen physicist to the rim of the Grand Canyon. The acceleration of gravity is 9.8 m/s2 .
Assuming no other external influences than gravity, in the horizontal direction (which we make to coincide with the x- axis) , speed is constant, so, applying the definition of average velocity, we can write the following equation:
Now, in the vertical direction (coincident with the y- axis) , as both movements are independent each other, initial velocity is zero, so we can write the following equation for the vertical displacement:
where Δh = -37.0 m , g = -9.8 m/s2
Solving (2) for t, we get:
Taking t₀ = 0, ⇒ Δt = t
Replacing (3) in (1), we get:
As the horizontal velocity is constant, the initial horizontal velocity is just the average one, i.e., 6.73 m/s.