Question

A falcon is soaring over a prairie, flying at a height of 49.0 m with a speed of 13.5 m/s. The falcon spots a mouse running along the ground and dives to catch its dinner. Ignoring air resistance, and assuming the falcon is only subject to the gravitational force as it dives, how fast will the falcon be moving the instant it is 5.00 m above the ground

Answer 1

32.3 m/s

Step-by-step explanation:

We can solve this problem by applying one of Newton's equations of motion:

`v^2 = u^2 + 2gs`

where v = final velocity of falcon

u = initial velocity of falcon

g = acceleration due to gravity (
`9.8 m/s^2`)

s = distance moved by falcon

From the question, we have that:

u = 13.5 m/s

s = initial height - new height = 49.0 - 5.0 = 44.0 m

Hence, to find the velocity when it has traveled 44 m towards the ground (5 m above the ground):

`v^2 = 13.5^2 + (2 * 9.8 * 44)\\\\\\v^2 = 182.25 + 862.4\\\\\\v^2 = 1044.65\\\\\\v = √(1044.65) \\\\\\v = 32.3 m/s`

The velocity of the falcon at the instant when it is 5.0 m above the ground is 32.3 m/s