Question

43.
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
A. 2:3
B. v3:2
C. V1:3
D. 13:1



Can someone please answer this

Answer 1

Answer:

C

Explanation:

we know, maximum height , h_{max}=\frac{u^2sin^2\theta}{2g}h

max

=

2g

u

2

sin

2

θ

given, \theta_1=30^{\circ}θ

1

=30

∘

\theta_2=60^{\circ}θ

2

=60

∘

h_1=\frac{u_1^2sin^2\theta_1}{2g}h

1

=

2g

u

1

2

sin

2

θ

1

= \frac{u_1^2sin^230^{\circ}}{2g}

2g

u

1

2

sin

2

30

∘

= \frac{u_1^2}{8g}

8g

u

1

2

......(1)

h_2=\frac{u_2^2sin^2\theta_2}{2g}h

2

=

2g

u

2

2

sin

2

θ

2

= \frac{u_2^2sin^260^{\circ}}{2g}

2g

u

2

2

sin

2

60

∘

= \frac{3u_2^2}{8g}

8g

3u

2

2

as, h_1=h_2h

1

=h

2

\frac{u_1^2}{8g}=\frac{3u_2^2}{8g}

8g

u

1

2

=

8g

3u

2

2

\frac{u_1}{u_2}=\frac{\sqrt{3}}{1}

u

2

u

1

=

1

3