What Is the Maximum Reaction Time for a Ranger to Avoid a Deer?

[jp0108]

Homework Statement

A ranger in a national park is driving at 47 kilometers per hour when a deer jumps onto the road 72 meters ahead the vehicle. After a reaction time of t (s), the ranger applies the brakes to produce an acceleration of -2.6 meters per second squared.

What is the maximum reaction time allowed if the ranger is to aviod hitting the deer? Answer in units of (s)


Vi = 47 km/h

d or delta x = 72

a = -2.6 m/s^2

delta t = ?

 

[marlon]

keep in mind that during the reaction period delta t, the velocity of the ranger is 47 km/hafter the delta t is passed, the velocity is reduced to 0 because of the negative acceleration -2.6

You really need to split up the question in 2 parts :

1) during the delta t
2) once the delta t is finished and the ranger is actually applying the break.
So, what formula's do you know to calculate velocity and position as a function of time ?Also, pay attention to the given UNITS !

marlon

 

[thomate1]

I would approach this problem by first converting all units to the same system. In this case, I would convert the initial velocity from kilometers per hour to meters per second, which would be 13.1 m/s. I would also convert the distance from meters to kilometers, which would be 0.072 km.

Next, I would use the formula d = Vi*t + 1/2*a*t^2 to solve for t, which represents the reaction time. Plugging in the values, we get 0.072 km = (13.1 m/s)*t + 1/2*(-2.6 m/s^2)*t^2. Simplifying this equation, we get t^2 - 5t + 0.028 = 0. Using the quadratic formula, we can solve for t and get two possible solutions: t = 0.032 seconds or t = 5 seconds.

However, since the ranger cannot have a negative reaction time, we can eliminate the first solution and conclude that the maximum reaction time allowed is 5 seconds. This means that the ranger must apply the brakes within 5 seconds after seeing the deer in order to avoid hitting it.

In conclusion, the maximum reaction time allowed for the ranger to avoid hitting the deer is 5 seconds. It is important for the ranger to be alert and react quickly in order to prevent accidents and protect both themselves and the animals in the national park.