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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 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.

A man is sitting on the shore of a river. He is in the line of a 1.0 m long 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.

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
6 years ago
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°.

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