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Grade: 12
        
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
2 months ago

Answers : (2)

Saurabh Koranglekar
askIITians Faculty
6641 Points
							576-319_IMG_20200328_190830.jpg
						
2 months ago
Vikas TU
11137 Points
							
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
2 months ago
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