Question

If two balls are projected at an angle of 60degree and 45º and the total heights reached are same then
their initial velocities are in the ratio of​

Answer 1

Answer:

hope it will help you.Only formula is used.

Answer 2

Their initial velocities are in the ratio of $\sqrt{2}:\sqrt{3}$.

Explanation:

The maximum height reached by the projectile is given by :

$H=\dfrac{u^2\sin ^2\theta}{2g}$

Let u₁ is the speed when it was projected by an angle of 60 degrees and u₂ is the speed when it was projected by an angle of 40 degrees. As their heights are same. So,

$\dfrac{u_1^2\sin ^2(60)}{2g}=\dfrac{u_2^2\sin^2(45)}{2g}\\\\(\dfrac{u_1}{u_2})^2=\dfrac{\sin ^2(45)}{\sin^2 (60)}\\\\(\dfrac{u_1}{u_2})^2=\dfrac{2}{3}\\\\\dfrac{u_1}{u_2}=\sqrt{\dfrac{2}{3}}$

So, their initial velocities are in the ratio of $\sqrt{2}:\sqrt{3}$.

Learn more,

Projectile motion

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