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A man is sitting on the shore of a river. He is in the line of a 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.

Sol. When the apple just touches the end B of the boat. 
x = 5 m, u = 10 m/s, g = 10 m/s2, θ = ? 
x = (u^2 sin⁡〖2 θ〗)/10 
⇒ 5 = (〖10〗^2 sin⁡〖2 θ〗)/10⇒ 5 = 10 sin 2 θ 
⇒ sin 2 θ = 1/2 ⇒ sin 30° or sin 150° 
⇒ θ = 15° or 75° 

Similarly for end C, x = 6 m 
Then 2 θ1 = sin–1 (gx/u2) = sin–1 (0.6) = 182° or 71°. 
So, for a successful shot, θ may very from 15° to 18° or 71° to 75°.