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Chapter 8: Q.18 (page 199)

A car drives over the top of a hill that has a radius of 50 m. What maximum speed can the car have at the top without flying off the road?

Short Answer

Expert verified

The maximum speed that the car can have without flying off the road is22.1m/s

Step by step solution

01

Given information

Given in the question that, A car drives over the top of a hill that has a radius of 50m.

02

Apply the equation of motion 

Let's consider the information given in the question

Car does not fly until force Ndoes not become zero or less than zero

N+mv2R=mg

Here,

mgindicates the weight of the car

Nshows the normal force acting on the car

mremains the mass of the car

vis the velocity of the car

role="math" localid="1648309282093" Rremains the radius of the circular path

When N=0

mv2R=mg

03

Apply the expression of velocity

From the information, we know that R=50mand g=9.8m/s2

mv2R=mg

Therefore,

鈬�v2R=g

鈬�V=gR

鈬�V=(9.8)(50)

鈬�V=490

鈬�V=22.136m/s

04

Final answer

The maximum speed that the car can have without flying off the road is22.1m/s

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