A hawk is flying horizontally at 10.0 m/sec in a straight line 200 m above the g

Question

A hawk is flying horizontally at 10.0 m/sec in a straight line 200 m above the ground. A mouse it was carrying is released from its grasp. The hawk continues on its path at the same speed for two seconds before attempting to retrieve its prey. To accomplish the retrieval, it dives in a straight line at a constant speed and recaptures the mouse 3.0 meters above the ground. Assuming no air resistance,
A) find the diving speed B) what angle did the hawk make with the horizontal during its descent? C) for how long did the mouse have the delusion of escape
Answers for A) 46.9 m/s, B) 77.7 degrees, C) 6.3 seconds

Explanation / Answer

when mouse was released it will only have horizontal velocity = 10 m/s

and no vertical velocity initially.

lets first find time at which mouse is at 3m above ground.

displacement of mouse = 3 - 200 = - 197 m (minus sign because of downward direction)

y = uy*t + ay*t^2/2

-197 = 0 - 9.81t^2/2

t = 6.34 sec

horizontal distance tarveled by mouse in this time,

x = vx *t = 10 x 6.34 =63.4 m

hawk reacts after 2 sec and in this hawk tarvels 10 x 2 = 20 m horizontally.

now it have to travel. (63.4-20)i + 197j in (6.34 -2) = 4.34 sec

speed = distance / time = sqrt(43.4^2 + 197^2) / 4.34

= 46.48 m/s ...........Ans(A)

(B) angle = tan^-1(197/43.4) = 77.6 deg below horizontal.

  

(C) as calculated above, t = 6.34 sec

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