Question

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 center 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.Concept of Physics - 1 , HC VERMA , Chapter "Rest and Motion : Kinematics

Answer 1

Solution:
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Minimum angle of projection:
x=5m
u=10m/s
θ=?
g=10m/s2
x=u²sin2θ/g
5=100sin2θ/10
sin2θ=5/10=1/2
sin2θ=1/2= sin30 or sin150
θ=15° or 75°

Maximum angle of projection:
x=6m
2θ=sin⁻¹[gx/u²]=sin⁻¹[10x6x10x10]=sin⁻¹[0.6]
=18° 0r 71°
so for a successful shot , θ may vary from 15° to 18° or 71° to 75°