Question

You have been hired as the Wildlife Protection Advisor for the Arizona Highway Patrol. The range of the veryrare Archimedean tortoise in the wild is currently restricted to a small patch of open desert, through which runsa long, straight road. Studies show that a driver at night can see a tortoise in the roadway 55 meters ahead.Your assignment is to determine what maximum night-time speed limit will give drivers sufficient time to braketo a halt in that distance. The typical coefficient of skidding friction of rubber against asphalt is 0.82

Answer 1

Given:

the distance of the tortoise is,

$d=55\text{ m}$

The coefficient of friction between the tyre and the asphault is,

$\mu=0.82$

The acceleration of the transport is,

$\begin{gathered} a=-\mu g \\ =-0.82\times9.8 \\ =-8.04m/s^{2^{}} \end{gathered}$

Now the final velocity after the brakes applied is 0.

we have to find the initial velocity.

we can write,

$0^2=v^2-2ad$

Substituting the values we get,

$\begin{gathered} 0^2=v^2-2\times8.04\times55 \\ v=\sqrt[]{2\times8.04\times55} \\ v=29.7\text{ m/s} \end{gathered}$

Hence the speed limit is 29.7 m/s.