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Two balls are projected from the same point in directions inclined at 60 and 30 to the horizontal. If they attain the same maximum height, the ratio of their velocities of projection is : A) 1 : 1 B) 1 : 2 C) 1 : p 3 D) p 3 : 1

Two balls are projected from the same point in
directions inclined at 60 and 30 to the
horizontal. If they attain the same maximum
height, the ratio of their velocities of projection
is :
A) 1 : 1 B) 1 : 2 C) 1 :
p
3 D)
p
3 : 1

Grade:12

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
576-319_IMG_20200328_190830.jpg
Vikas TU
14149 Points
4 years ago
Dear student 
Given-
θ1=30°
θ2=60°
# Formula-
- Height-
H = u^2.(sinθ)^2 / 2g
- Range-
R = u^2.sin2θ / g
# Calculations-
Let u1 and u2 be the initial velocities for angle 30° and angle 60°.
a) When range is same,
R1 = R2
u1^2.sin60/g = u2^2.sin120/g
u1^2×0.866 = u2^2×0.866
u1 = u2
u1/u2 = 1
b) When heights are same,
H1 = H2
u1^2.(sin30)^2/2g = u2^2.(sin60)^2/2g
u1^2×(0.5)^2 = u2^2×(0.866)^2
0.25×u1^2 = 0.75×u2^2
u1^2 = 3×u2^2
u1/u2 = √3

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