Question

9. Two bullets are fired at angle 8 and (90-0) to the horizontal with same speed. The ratio
flight is
a. 1:1
b. tano:1
c. 1:tano

d. tan²0:1​

Answer 1

ㅤ$\;\;\underline{\textbf{\textsf{ Given :-}}}$

• Two bullets are fired at angle $\theta$ and

(90-$\theta$ ) to the horizontal with same speed.

• $\sf{\theta_1=\theta}$

• $\sf{\theta_2=90^o-\theta}$

ㅤ$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• The ratio of time flight

ㅤ$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

We know that :-

Time of flight of a projectile is given by

$\sf{\dashrightarrow T=\dfrac{2u\sin\theta}{g}}$

For same speed :-

$\sf{\dashrightarrow T\propto\sin\theta}$

$\sf{\dashrightarrow \dfrac{T_1}{T_2}=\dfrac{\sin\theta_1}{\sin\theta_2}}$

$\sf{\dashrightarrow \dfrac{T_1}{T_2}=\dfrac{\sin\theta}{\sin(90^o-\theta)}}$

$\sf{\dashrightarrow \dfrac{T_1}{T_2}=\dfrac{\sin\theta}{\cos\theta}}$

$\sf{\dashrightarrow \dfrac{T_1}{T_2}=\tan\theta}$

$\bf{\dashrightarrow \underline{\:\underline{\green{\:T_1:T_2=\tan\theta:1}}\:}}$

ㅤ$\;\;\underline{\textbf{\textsf{Hence -}}}$

$\underline{\textsf{ Correct option </p><p>\textbf{( b)}}}$

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