Question

A kestrel dives from a stationary hover, 20 m above the ground, to catch its prey, typically mice, on the ground. (a) If the kestrel’s acceleration toward the ground is due solely to free fall, calculate how long it takes to reach the ground. (3 points) (b) A field mouse can run at a top speed of 10 km/h, which it achieves starting from rest in 1 s. Assuming that the only way for the mouse to survive the kestrels attack is to find shelter, calculate the maximum distance the mouse can be from shelter to survive if it sees the kestrel as it begins its dive. (3 points) The mouse, in fact, only first sees the kestrel when it is at the mid point of the dive 10m above the ground. (c) Based only on your intuition (and not on any calculation), estimate how far the mouse needs to be from shelter to survive now. (1 point) (d) Calculate how far the mouse needs to be from shelter to survive in the new situation.

Answer 1

a)
Initial velocity, u = 0
Distance travelled, h = 20 m
Using the formula, h = ut + 1/2 gt²,
20 = 0 + 0.5 x 9.81 x t²
t = SQRT[20/4.905]
= 2.02 s

b)
10 km/hr = 2.78 m/s
Time taken by the kestrel to reach ground is,
2.02 s

Acceleration of mouse, a = v/t        [Since initial velocity = 0]
= 2.78/1 = 2.78 m/s²
Distance travelled by the mouse in 1 s is,
s = u + at
= 0 + 2.78 x 1
= 2.78 m.

Now the mouse has 2.02 - 1 = 1.02 s remaining.
Distance travelled in 1.02 s = vt
= 2.78 x 1.02
= 2.83 m

Total distance the mouse can travel in 2.02 s is
2.78 + 2.83
= 5.61 m

c)
Half of the previous part, ie 2.8 m

d)
Time taken by the kestrel to reach 10 m is,
t1 = SQRT[10/4.905] = 1.43 s
Time taken by the kestrel to reach ground from 10 m is,
2.02 - 1.43
= 0.591 s

Acceleration of mouse, a = 2.78 m/s²
Distance travelled by the mouse in 0.591 s is,
s = u + at
= 0 + 2.78 x 0.591
= 1.64 m.