Question

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

The maximum speed that the car can have without flying off the road is$22.1m/s$

Step-by-step solution

Given information

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

Apply the equation of motion 

Let's consider the information given in the question

Car does not fly until force $N$does not become zero or less than zero

$N+\frac{m{v}^2}{R}=mg$

Here,

$mg$indicates the weight of the car

$N$shows the normal force acting on the car

$m$remains the mass of the car

$v$is the velocity of the car

role="math" localid="1648309282093" $R$remains the radius of the circular path

When $N=0$

$\frac{m{v}^2}{R}=mg$

Apply the expression of velocity

From the information, we know that $R=50m$and $g=9.8m/s^2$

$\frac{m{v}^2}{R}=mg$

Therefore,

$\Rightarrow \frac{v^2}{R}=g$

$\Rightarrow V=\sqrt{gR}$

$\Rightarrow V=\sqrt{\left(9.8\right)\left(50\right)}$

$\Rightarrow V=\sqrt{490}$

$\Rightarrow V=22.136\mathrm{m}/\mathrm{s}$

Final answer

The maximum speed that the car can have without flying off the road is$22.1m/s$