Question

Two balls are protected from the same point in directions 30°and 60° with respect to the horizontal.what is the ratio of their initial velocities if they a) attain the same height ? b) have the same range

Answer 1

Hii dear,

# 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.