How Far Can a Tourist Run Before a Bear Catches Up?

[ayerski]

Homework Statement

A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 4.0m/s. The car is a distance d away. The bear is 26 m behind the tourist and running at 6.0 m/s. The tourist reaches the car safely. What is the maximum value for d?

Homework Equations

v = d/t

The Attempt at a Solution

I've been trying to use multiple variables to solve but i just can't seem to figure out a strategy.

 

[ryan88]

To solve this question you need to work out how long the bear would take to catch up to the tourist, and then use this time and the tourists speed to figure out the distance between him and the car.

Hope that helps.

Ryan

 

[tomcue]

As a scientist, the first step in solving this problem would be to clearly define the variables and their relationships. In this case, we have the tourist's speed (4.0 m/s), the bear's speed (6.0 m/s), and the distance between the bear and the tourist (26 m). We also have the distance between the tourist and the car (d), which is the unknown variable we are trying to solve for.

To find the maximum value for d, we can use the equation v=d/t, where v is the speed and t is the time. In this case, we can set up two equations: one for the tourist and one for the bear.

For the tourist, we have v=d/t, where v=4.0 m/s and t is the time it takes for the tourist to reach the car. We can rearrange this equation to solve for t: t=d/v.

For the bear, we have v=d/t, where v=6.0 m/s and t is the time it takes for the bear to reach the tourist. We can rearrange this equation to solve for t: t=d/v.

Since both the tourist and the bear reach their respective destinations at the same time, we can set these two equations equal to each other: d/v = d/v.

Solving for d, we get d=4.0t for the tourist and d=6.0t for the bear. Since the tourist reaches the car safely, we know that d must be greater than 26 m (the initial distance between the bear and the tourist). Therefore, we can set up the inequality 4.0t > 26.

Solving for t, we get t > 6.5 seconds. Plugging this value back into our equations for d, we get d > 26 m.

Therefore, the maximum value for d is greater than 26 m, and specifically it is d > 26 m + 4.0*6.5 seconds = 52 m.

In conclusion, the maximum value for d is 52 m, meaning that the tourist must have been at least 52 meters away from his car when he started running from the bear in order to reach it safely. This information could be helpful in determining safe distances for tourists to keep from wild animals in certain areas.