Two objects are thrown up at angles of 45° and 60° respectively, with the horizontal. If both objects attain same vertical height, then the ratio of magnitude of velocities with which these are projected is

Question

Two objects are thrown up at angles of 45° and 60° respectively, with the horizontal. If both objects attain same vertical height, then the ratio of magnitude of velocities with which these are projected is (A) √(5/3) (B) √(3/5) (C) √(2/3) (D) √(3/2)

Tardigrade Admin · Accepted Answer

h1=h2 (u12 sin 2 45°/2 g)=(V22 sin 2 60°/2 g) (u12/V22)=((√3/2) × (√3/2)/(1)2)=(3/2) (V1/V2)=√(3/2)

Q. Two objects are thrown up at angles of $4 5^{\circ}$ and $6 0^{\circ}$ respectively, with the horizontal. If both objects attain same vertical height, then the ratio of magnitude of velocities with which these are projected is

$\frac{5}{3}$

$\frac{3}{5}$

$\frac{2}{3}$

$\frac{3}{2}$

$h_{1} = h_{2}$
$\frac{u _{1}^{2} s i n ^{2} 4 5 ^{\circ}}{2 g} = \frac{V _{2}^{2} s i n ^{2} 6 0 ^{\circ}}{2 g}$
$\frac{u _{1}^{2}}{V _{2}^{2}} = \frac{\frac{3}{2} \times \frac{3}{2}}{\frac{1}{2}} = \frac{3}{2}$
$\frac{V _{1}}{V _{2}} = \frac{3}{2}$

Q. Two objects are thrown up at angles of 45∘ and 60∘ respectively, with the horizontal. If both objects attain same vertical height, then the ratio of magnitude of velocities with which these are projected is

35​​

53​​

32​​

23​​