Question 36 of 308

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed $v$, he sees that rain drops coming at an angle ${60}^{^{\circ}}$ from the horizontal. On further increasing the speed of the car to $\left(1+\beta \right)v$, this angle changes to ${45}^{^{\circ}}$. The value of $\beta$ is close to :

A$0.50$B$0.41$C$0.37$D$0.73$

Show answer and solution▾

Answer: (D) $0.73$

$\tan =60^{\circ}=\dfrac{{v}_{rg}}{v}$ ........$\left(1\right)$
$\tan 45^{\circ}=\dfrac{{v}_{rg}}{(\beta +1)v}$ ..........$\left(2\right)$
$\sqrt{3}v=(\beta +1)v$
$\beta =\sqrt{3}-1=0.732$