A hawk is flying horizontally at 15.0 m/s in a straight line, 230 m above the gr

Question

A hawk is flying horizontally at 15.0 m/s in a straight line, 230 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

Explanation / Answer

Part A:

Step 1: After mouse starts free falling, Vertical distance traveled by mouse will be before catching back by hawk = 230 m - 3 m = 227 m

Now Using 2nd kinematic rule:

y = U*t + 0.5*a*t^2

U = initial Velocity of mouse = 0 m/sec, as mouse is in free fall

a = g = 9.81 m/sec^2

y = 227 m

So,

227 = 0*t + 0.5*9.81*t^2

t = sqrt (227/(0.5*9.81))

t = 6.80 sec (Also this is answer of part C.)

Now given that hawk starts diving 2.00 sec after mouse starts free falling, So

So diving time of Hawk = 6.80 - 2.00 = 4.80 sec

Now since hawk catches back mouse 3 m above the ground, So

Vertical displacement of Hawk = 230 - 3 = 227 m

Horizontal displacement of hawk will be

Horizontal displacement = Horizontal Speed*diving time

Remember that there is no acceleration in horizontal direction, So hawk's horizontal speed will be constant, using this

Horizontal displacement = 15*4.80 = 72 m

Now diving speed will be

diving speed = Total displacement/total time

Total displacement, s = 72 i + 227 j

|s| = sqrt (72^2 + 227^2)

|s| = 238.14 m

time = 4.80 sec

So,

diving speed = 238.14/4.80 = 49.6 m/sec

Part B.

direction of hawk during decent will be

direction = arctan (sy/sx)

direction = arctan (227/72) = 72.40 deg below the horizontal

(See that since its mentioned that angle should be below the horizontal, So answer should be a positive number, but if it doesn't work than try final answer as angle = -72.40 deg)

Part C.

As solved in part A,

free fall time of mouse = 6.80 sec

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Comment below if you have any doubt.

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