How Fast and at What Angle Must a Hawk Dive to Recapture Its Prey?

[Melchior25]

Homework Statement

A hawk is flying horizontally at 14.0 m/s in a straight line, 250 m above the ground. A mouse it has been carrying struggles free from its grasp. The hawk continues on its path at the same speed for 2.00 s before attempting to retrieve its prey. To accomplish the retrieval, it dives in a straight line at constant speed and recaptures the mouse 3.00 m above the ground.

(a) Assuming no air resistance, find the diving speed of the hawk.
m/s
(b) What angle did the hawk make with the horizontal during its descent?
° (below the horizontal)
(c) For how long did the mouse "enjoy" free fall?
s

Homework Equations

h=(.5)gt^2
vf=vi+at

xf=vxi*t

The Attempt at a Solution

for (a) I used h=(.5)gt^2 and solved for t. t=7.09987 s
I then plugged t into vf=vi+at to get a final v of 83.6497m/s diving speed for the hawk. Does this look right?

For (b) I'm lost on where to start. I drew a triangle and have a y height of 247. I also have a 90 degree angle. I don't know however how to solve for the angle.

For (c) I was going to use xf=vxi*t. Knowing my xf already and initial velocity once I figure out the angle from part (b).

Please help. I'm so lost.

 

[Melchior25]

So I figured out part a and part c but I'm struggling with art b. A is 50.0297 m/s and the time the hawk dove was 5.09987 s. I multiplied these two and got my hyp. I also know my y length. I drew a triangle and thought I calculated theta but my answer is wrong.