Question

A car is going at a speed of $6\text{m/s}$ when it encounters a $15\text{m}$ slope of angle ${30}^{\circ }$. The friction coefficient between the road and the tyre is $0.5$. The driver applies the brakes.
The minimum speed of the car with which it can reach the bottom is around $(g=10{\text{m/s}}^2)$

• A. $4\text{m/s}$
• B. $3\text{m/s}$
• C. $7.49\text{m/s}$
• D. $8.45\text{m/s}$

Answer 1

The correct option is C $7.49\text{m/s}$

When brakes are applied the forces on the car along the incline plane will be: 1) Force due to kinetic friction up the incline
2) a component of the gravitational force down the incline.
$F=ma=mg\sin \theta -\mu mg\cos \theta$
$a=g\sin \theta -\mu g\cos \theta$
$g\sin \theta =10\sin {30}^{\circ }=5{\text{m/s}}^2$
and $\mu g\cos \theta =0.5\times 10\times \cos {30}^{\circ }=4.33{\text{m/s}}^2$
$\therefore$ Minimum acceleration down the plane can be
$a=5-4.33=0.67{\text{m/s}}^2$
Minimum speed when it reaches the bottom can be
$v^2=u^2+2as$
$=(6{)}^2+2\times 0.67\times 15=56.1$
$\therefore v=7.49\text{m/s}$
Hence, the correct answer is option (c).