• A hawk is flying horizontally at 10 m/s in a straight line, 200 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 seconds before attempting to retrieve its prey. To accomplish the retrieval, it dives in a straight line at constant speed and recaptures the mouse 3 m above the ground. (a) Assuming no air resistance, find the diving speed of the hawk.
  • (b) What angle did the hawk make with the horizontal during its descend?
  • (c) For how long did the mouse “enjoy” free fall?

Before the hawk recaptures the mouse it moved 200-3=197m. No since the hawk was moving horizontally while leaving the rat, so there will be no component along the virtical direction. So the mouse will fall like free fall in (that is with g acceleration) in virtical direction. Now let us consider that mouse falling freely for t second then we have
12gt2=ht=2hg=2×1979.8=6.43s
Now since there is not resistance the mouse will also continue to move in the same horizontal speed. So it will move 200×6.43=1268m. The hawk started moving down after two second and by that time hawk had moved 400m horizontally. So the hawk have to move 1268-400=868m horizontally and 197m downwards, i.e. 8682+1972=890.07m. Now the hawk have to cover this distance in 6.43-2=4.43m. So the velocity of the hawk should be 890.074.43=205.09m/s. And the angle of the velocity is tan-1197890.09=12.88.

(a) The diving speed of the hawk is 205.09m/s

(b) It will make 12.88 degree downwards from horizontal.

(c) The mouse will enjoy 6.43s free fall.

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