Question

A car is going at a speed of 21.6 km/hr when it encounters a 12.8 m long slope of angle 30°. The friction coefficient between the road and the tyre is 1/2√3. Show that no matter how hard the driver applies the brakes, the car will reach the bottom with a speed greater than 36 km/hr. Take g=10 m/s².

Answer 1

Speed of the Car = 21.6 km/hr = 6 m/s.

Now, On the Incline,

mgsin30° - μmgcos30° = ma

⇒ g/2 - g/4 = a

⇒ g/4 = a

∴ a = 2.5 m/s².

Now, v² - u² = 2aS

⇒ (v)² - 6² = 2 × 2.5 × 12.8

⇒ v² = 64 + 36

⇒ v² = 100 m/s.

∴ v = 10 m/s.

or v = 36 km/hr.

This is the minimum speed which can be reached by the car while moving down.

Hope it helps.