Motion in a plane NCERT Solutions Class 11 Physics - Solved Exercise Question 4.15

Question 4.15:

The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m s-1 can go without hitting the ceiling of the hall ?

Solution:

Speed of the ball, u = 40 m/s
Maximum height, h = 25 m
In projectile motion, the maximum height reached by a body projected at an angle θ, is given by the relation:
h = u2 Sin2θ / 2g
25 = (40)2 Sin2θ / 2 X 9.8

sin2 θ = 0.30625
sin θ = 0.5534
θ = sin–1(0.5534) = 33.60°
Horizontal range, R = u2 Sin 2θ / g
= (40)2 X Sin (2 X 33.600) / 9.8
= 1600 X Sin (67.2) / 9.8
= 1600 X 0.922 / 9.8  =  150.53 m

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