Finding position given displacement, velocity

In summary, the problem is asking how close to the finish line the hare can stop and taunt the tortoise before continuing the race, and which animal will win in a photo finish. The hare runs at 1.00m/s for 0.800 km before stopping, while the tortoise crawls at 0.900m/s for the entire 3.70km. The hare can use kinematic equations with an acceleration of 0 to determine the distance it can stop before the finish line, but this only works once it starts moving again.
  • #1
steph35
11
0

Homework Statement


A hare and tortoise compete in a race over a course of 3.70km long. The tortoise crawls straight and steadily at its max speed of .900m/s toward the finish line. The hare runs at its max speed of 1.00m/s toward the goal for .800 km and then stops to taunt the tortoise. Assume that, when moving, both animals move steadily at their respective max speed.


Homework Equations


How close to the goal can the hare let the tortoise approach before resuming the race, which tortoise wins in a photo finish?


The Attempt at a Solution


I drew the picture but couldn't get anywhere. I thought that i would have to use a kinematic equation but not all the givens are given...
 
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  • #2
You can use kinematic equations. a=0, which should simplify things for you.

Note, for the hare this only works once it starts moving again.
 
  • #3


I would approach this problem by using the equations of motion to determine the position of both the hare and tortoise at different points in time. The displacement of an object can be calculated by multiplying its velocity by the time it has been moving. In this case, we can calculate the displacement of the hare after it has run for 0.8 km at 1.00 m/s, which would be 800 m. We can also calculate the displacement of the tortoise after it has crawled for 3.70 km at 0.900 m/s, which would be 3330 m.

Next, we can use the formula v = d/t to calculate the time it takes for each animal to cover their respective distances. For the hare, this would be 800 m / 1.00 m/s = 800 seconds. For the tortoise, it would be 3330 m / 0.900 m/s = 3700 seconds.

Now, we can use the equation x = x0 + vt to determine the position of each animal after the given time has passed. For the hare, this would be x = 0.8 km + 1.00 m/s * 800 seconds = 0.8 km + 800 m = 1.6 km. For the tortoise, it would be x = 0 km + 0.900 m/s * 3700 seconds = 0 km + 3330 m = 3.33 km.

From this, we can see that the hare would be 1.6 km from the finish line when it stops to taunt the tortoise. Therefore, the tortoise would need to crawl 1.6 km in order to catch up and win the race in a photo finish. However, since the hare has a head start of 800 m, the tortoise would actually need to crawl 1.6 km - 0.8 km = 0.8 km to catch up and win the race.

In conclusion, the hare can let the tortoise approach within 0.8 km of the finish line before resuming the race and still win in a photo finish.
 

What is the difference between displacement and position?

Displacement is the change in an object's position from its starting point, while position refers to the exact location of an object in space.

How do you calculate position given displacement and initial position?

To calculate position, you add the displacement to the initial position. This gives you the final position of the object.

Can you have a negative position or displacement?

Yes, both position and displacement can have negative values. A negative displacement indicates that the object has moved in the opposite direction of its initial position. A negative position indicates that the object is located in the negative direction of a chosen reference point.

What is the relationship between velocity and change in position?

Velocity is a measure of an object's speed and direction of motion. The change in position is directly related to the velocity of an object. A higher velocity means a larger change in position over time.

How does time affect the calculation of position given displacement and velocity?

Time is a crucial factor in calculating position using displacement and velocity. The longer the time interval, the greater the change in position will be. Additionally, the direction of velocity also affects the final position, as the object may have changed direction during the given time interval.

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