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

`(1)/(2)*(9.8 \, (m)/(s^(2)))*(t \, s)^(2) = (15 \, m) \\ t= \sqrt{ (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= (1)/(2) *(a \, (m)/(s^(2)) )*(1.75 \, s)^(2) = (1)/(2)( (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)