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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

6 months ago

Answers : (2)

Saurabh Koranglekar
askIITians Faculty
8397 Points
							576-319_IMG_20200328_190830.jpg
						
6 months ago
Vikas TU
12159 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
5 months ago
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