Question

Two balls are projected in directions at 30° and 60°with the horizontal. If both attains the same
height, the ratio of their initial speeds is​

Answer 1

Explanation:

If two balls are projected at 45 and 60 degree angles and both reached the same height, what is the ratio of initial velocities?

Let U(45) = the initial velocity of the ball launched at 45 degrees and let U(60) = the initial velocity of the ball launch at 60 degrees.

Formula for Max_dy = u²sin²θ/2g

Max_dy = u²(45) * sin²45/2g

Max_dy = u²(60) * sin² 60/2g

Solving for the ratio of U(45) / U(60)

u²(45) * sin²45/2g = u²(60) * sin² 60/2g

U²(45) * 0.5/2g = u²(60) * 0.75/2g

U²(45) = u²(60) * 0.75/2g / 0.5/2g

U²(45) = u²(60) * 0.75 / 0.5 and extracting the square roots

U(45) = U(60) * sqrt(3/2)

U(45)/U(60) = sqrt(3/2)