Two similar balls A and B are projected at a time with the same velocity at angles 30° and 60° resp. The ratio of the heights reached by them is?
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Answer:
# 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
Hope that helped you...
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