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

  • Thread starter ayerski
  • Start date
Olivia are discussing a problem involving a tourist being chased by an angry bear. The tourist is running at 4.0m/s towards his car, which is a distance d away. The bear, who is 26m behind the tourist, is running at 6.0m/s. Ryan suggests using the equation v = d/t to solve the problem, but Olivia is struggling to come up with a strategy. In summary, Olivia needs to calculate the time it would take for the bear to catch up to the tourist, and then use that time and the tourist's speed to determine the maximum distance d between the tourist and his car.
  • #1
ayerski
4
0

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.
 
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  • #2
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
 
  • #3


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.
 

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

1. What should I do if I encounter a bear while on a hike?

If you encounter a bear while on a hike, the most important thing to remember is to stay calm and avoid any sudden movements. Slowly back away while facing the bear and give it plenty of space to move away. Do not run or climb a tree, as these actions may provoke the bear.

2. How can I prevent a bear encounter while camping?

The best way to prevent a bear encounter while camping is to properly store all food and scented items in a bear-proof container or hung from a tree at least 10 feet above the ground. Also, avoid cooking and eating in or near your tent, and do not leave any food scraps or garbage around your campsite.

3. What should I do if a bear approaches my campsite?

If a bear approaches your campsite, stay calm and try to make yourself look as large as possible by standing up and spreading your arms. Make loud noises and bang pots and pans together to scare the bear away. If the bear does not leave, slowly back away and seek shelter in your car or a nearby building.

4. Can bear spray effectively deter a bear attack?

Bear spray can be an effective deterrent in a bear attack, but it is important to use it properly. Make sure to aim for the bear's face and spray in short bursts. Also, be aware of the wind direction to avoid getting the spray in your own face. Bear spray should only be used as a last resort in a life-threatening situation.

5. What should I do if a bear charges at me?

If a bear charges at you, it may be a bluff charge to scare you away. Stand your ground and make loud noises while slowly backing away. If the bear continues to charge, use bear spray or any available objects (such as a stick or rock) to defend yourself. If the bear makes contact, play dead by lying on your stomach with your hands clasped behind your neck and your legs spread apart to make it harder for the bear to flip you over. Stay still until the bear leaves the area.

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