Question

A fox is 7 meters from the base of a tree that is 15 m tall. A nest of owls is at the top of the tree. One of the owlets tosses a piece of meat horizontally from the nest at 1.2 m/s. The fox runs to catch the meat just before it hits the ground. What is the speed of the fox just as he catches the meat?

Answer 1

Refer to the diagram shown below.

In this analysis, wind resistance is ignored, and g = 9.8 m/s².

The meat falls with zero vertical velocity, therefore the time, t, before the meat hits the ground is
$\frac{1}{2}*(9.8 \, \frac{m}{s^{2}})*(t \, s)^{2} = (15 \, m) \\ t= \sqrt{ \frac{15}{4.9} }= 1.75 \, s$

If the fox catches the meat before it hits the ground, then the fox should travel a horizontal distance d in the same time that the meat travels a horizontal distance (7 -d).
The meat travels a distance of 
7 - d = (1.2 m/s)*(1.75 s) = 2.1 m
or
d = 4.9 m

Let v =  velocity of the fox when it catches the meat.
If the acceleration of the fox is a m/s², then
v = 1.75a
Also,
$d= \frac{1}{2} *(a \, \frac{m}{s^{2}} )*(1.75 \, s)^{2} = \frac{1}{2}( \frac{v}{1.75})^{2}*(1.75^{2}) \\ 4.9 = 0.875v^{2} \\ v^{2} = 5.6 \\ v = 2.366 \, m/s$

Answer:  2.37 m/s  (nearest hundredth)