Sitting on the shore of a river, a man 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 is able to throw the apple only with a speed of 10 m/s , determine the minimum and maximum angles of projection for a successful shot. Assume that the point of projection and the edge of the boat are in the same horizontal level. (Take g = 10 m/s ^2

Step-by-step solution

The distance of the centre of the boat from the man is 5.5 m and its length is 1.0 m . The nearest and farthest edges of the boat are at distances 5.5 - 0.5 = 5.0 m and 5.5 + 0.5 = 6.0 m respectively. For a successful shot, the range R of the projectile must satisfy 5.0 R 6.0 . The range of a projectile is given by R = v^2 2 g . Substituting v = 10 m/s and g = 10 m/s ^2 , we get: R = 10^2 2 10 = 10 2 Therefore, the inequality becomes: 5.0 10 2 6.0 0.5 2 0.6 The principal values for 2 are between 30^ and 37^ . Since