Solve Collision Question: Will Sue's Car Hit the Van?

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In summary, Speedy Sue, driving at 32.0 m/s, enters a one-lane tunnel and observes a slow-moving van 160 m ahead traveling at 5.20 m/s. Sue can only accelerate at -2.00 m/s2 due to the wet road. It is determined that there will be a collision, but it is unclear how far into the tunnel and at what time it will occur. If Sue starts braking immediately, it is necessary to use the final position function to calculate how far into the tunnel she will come to a stop and how long it will take her to brake. The distance the van has travelled is also unknown.
  • #1
physics_geek
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collision question!

Speedy Sue, driving at 32.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 160 m ahead traveling with velocity 5.20 m/s. Sue applies her brakes but can accelerate only at -2.00 m/s2 because the road is wet. Will there be a collision?



If yes, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of closest approach between Sue's car and the van and enter zero for the time.




i already know there will be a collision
but I am not sure how to calculate how far into the tunnel it will happen

im guessin to use the final position function..but i dunno
 
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  • #2


If Sue starts braking immediately after entering the tunnel, how far into the tunnel will she have come to a stop?
How long will it take her to brake? What is then the distance the van has travelled?
 
  • #3
how to plug in the numbers

I would approach this problem by first analyzing the given information and identifying the key variables involved. In this case, we have Sue's initial speed (32.0 m/s), the van's initial speed (5.20 m/s), and Sue's acceleration (-2.00 m/s2). We also know that the distance between Sue's car and the van is 160 m.

Next, I would use the equations of motion to calculate the time it takes for Sue's car to reach the van's position. We can use the equation s = ut + 1/2at^2, where s is the final position, u is the initial velocity, a is the acceleration, and t is the time. Plugging in the given values, we get:

160 m = (32.0 m/s)t + 1/2(-2.00 m/s2)t^2

Simplifying, we get the quadratic equation -2.00t^2 + 32.0t - 160 = 0. Solving for t using the quadratic formula, we get t ≈ 5.57 seconds.

This means that it will take Sue's car approximately 5.57 seconds to reach the van's position. Now, we can use the equation v = u + at to calculate the final velocity of Sue's car at the time of the collision. Plugging in the values, we get:

v = 32.0 m/s + (-2.00 m/s2)(5.57 s) = 21.86 m/s.

Since the van is traveling at a speed of 5.20 m/s, the relative velocity between Sue's car and the van at the time of collision is 21.86 m/s - 5.20 m/s = 16.66 m/s.

To determine the distance into the tunnel where the collision occurs, we can use the equation s = ut + 1/2at^2 again. However, this time we are solving for s. Plugging in the values, we get:

s = (32.0 m/s)(5.57 s) + 1/2(-2.00 m/s2)(5.57 s)^2 = 88.96 m.

Therefore, the collision will occur approximately 88.96 meters into the tunnel. We can also use the equation s = ut + 1/
 

FAQ: Solve Collision Question: Will Sue's Car Hit the Van?

1. What factors determine if Sue's car will hit the van?

The main factors that determine if Sue's car will hit the van are the speed and direction of both vehicles, the distance between them, and any potential obstacles or road conditions that may affect their movements.

2. Can Sue's car avoid hitting the van if she slams on the brakes?

It depends on the speed and distance between the two vehicles. If Sue's car is traveling at a high speed and is too close to the van, slamming on the brakes may not be enough to avoid a collision. However, if there is enough distance between them, braking could be effective in preventing a collision.

3. How can we calculate the chances of a collision between Sue's car and the van?

The chances of a collision can be calculated by considering the speed and direction of both vehicles, their distance from each other, and any potential obstacles or road conditions. Using this information, we can estimate the likelihood of a collision occurring and take appropriate precautions.

4. Is there a way to predict if Sue's car will hit the van?

While it is impossible to predict with 100% certainty, using the factors mentioned above, we can make an educated guess about the likelihood of a collision occurring. However, external factors such as sudden changes in road conditions or unexpected obstacles can also play a role, making it difficult to make a definite prediction.

5. What should Sue do if she realizes her car will hit the van?

If it is safe to do so, Sue should try to steer her car away from the van to avoid a direct collision. She should also try to slow down her car as much as possible to reduce the impact. However, if there is no way to avoid a collision, she should remain calm and brace for impact.

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