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

Time of flight of a projectile is given by,

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

where $\sf{u}$ is initial velocity and $\theta$ is angle of projection.

For same speed $\sf{u,}$ we get,

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

Therefore,

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

According to the question,

• $\sf{\theta_1=\theta}$

• $\sf{\theta_2=90^o-\theta}$

Then,

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

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

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

$\sf{\longrightarrow\underline{\underline{T_1:T_2=\tan\theta:1}}}$

Hence (b) is the answer.