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Question
A man is sitting on the shore of a river. He is in the line of 1.0 m long boat and is 5.5 m away from the centre of the boat. He wishes to throw an apple into the boat. If he can throw the apple only with a speed of 10 m/s, find the minimum and maximum angles of projection for successful shot. Assume that the point of projection and the edge of the boat are in the same horizontal level.
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Solution
Given:
Length of the boat = 1.0 m
Distance between the man and the centre of the boat (R) = 5.5 m
Initial speed (u) of throwing the apple by the man = 10 m/s
Acceleration due to gravity (g) = 10 m/s2
We know that the horizontal range is given by
R = `(u^2 sin 2alpha)/g`
⇒ `5 = ((10)^2 sin 2 alpha)/10`
⇒ `sin 2 alpha = 1/2`
⇒ α = 15° or 75°
Similarly, for the endpoint of the boat, i.e., point C, we have:
Horizontal range (R) = 6 m
R = `(u^2 sin 2alpha)/g`
⇒ `6 = ((10)^2 sin 2 alpha)/10`
⇒ `sin 2 alpha = 3/5`
⇒ α = 18° or 71°
For a successful shot, the angle of projection α with an initial speed of 10 m/s may vary from 15° to 18° or from 71° to 75°. The minimum angle is 15°, and the maximum angle is 75°, but there is an interval of 53° for which the successful shot is not allowed. We can show this by putting the successive value of α from 15° to 75°.
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