A boy sitting at the rear end of a railway compartment of a train, running at a constant acceleration on horizontal rails, throws a ball towards the fore end of the compartment with a muzzle velocity of 20 m/sec at an angle 37º above the horizontal, when the train is running at a speed of 10 m/sec. If the same boy catches the ball without moving from his seat and at the same height of projection, find the speed of the train at the instant of his catching the ball. [ g = 10 m/sec 2 ; sin 37º = 3/5 ]
Text Solution
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42 m/s
Sol. t = 0
= 
+ 
= 20 cos 37 o 
+ 20 sin 37 o 
= 20 × 
+ 20 × 
= 16 
+ 12 
= 10 
∴ 
= 26 
+ 12 
At t = 0 x b = 0 x t = 0
Let they meet after time t
X b(t) – X b(0) = 26 t
X train(t) – X train(o) = 10t + 
at 2
Let The ball return to train after time t
∴ t = 
t = 
= 
s
X b(t) = X train (t)
∴ 26.t =10 t + 
at 2
16 = 
at
= a = 
m/s 2
V train(t) = 10 + at.
V train (t) = 10 + 
× 
= 10 + 32 = 42 m/s
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