Projectiles A and B are thrown at angles of 45° and 60° with the vertical, respectively, from the top of a 400 m high tower. If their ranges and times of flight are the same, the ratio of their speeds of projection is

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Solution

Q.
Projectiles A and B are thrown at angles of 45° and 60° with the vertical, respectively, from the top of a 400 m high tower. If their ranges and times of flight are the same, the ratio of their speeds of projection $v_{A} : v_{B}$ is [2024].

1 $1 : \sqrt{3}$

2 $\sqrt{2} : 1$

3 $1 : 2$

4 $1 : \sqrt{2}$

Ans.
(4)

$R_{A} = R_{B}$

$(V_{A} \cos 45 °) T = (V_{B} \cos 60 °) T$

$\frac{V_{A}}{\sqrt{2}} = \frac{V_{B}}{2}$

$\frac{V_{A}}{V_{B}} = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}$

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