Understanding t_max in the Drag Racer Problem

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In summary, the problem involves a car driving towards a dragster that is accelerating away from it. The first question asks for the maximum time (t_max) that the car could potentially hit the dragster if it continues at its initial velocity. The second question asks for the distance between the car and the dragster when the dragster starts accelerating at the last possible instant. However, due to the dragster's constant acceleration, it is not possible for the car to ever hit the dragster, making the second question difficult to answer.
  • #1
jcsp101
Problem:
To demonstrate the tremendous acceleration of a top fuel drag racer, you attempt to run your car into the back of a dragster that is "burning out" at the red light before the start of a race. (Burning out means spinning the tires at high speed to heat the tread and make the rubber sticky.)

You drive at a constant speed of v_0 toward the stopped dragster, not slowing down in the face of the imminent collision. The dragster driver sees you coming but waits until the last instant to put down the hammer, accelerating from the starting line at constant acceleration, a. Let the time at which the dragster starts to accelerate be t=0.

Question 1:
What is t_max, the longest time after the dragster begins to accelerate that you can possibly run into the back of the dragster if you continue at your initial velocity?

My Question:
What does the problem mean by t_max?
is it like the time when the drag racer and car touch, or when they both reach their max velocity, or what?
 

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  • #2
The drag racer is accelerating away from the car while the car ismoving towards it at a constant velocity, so the question asks, as I interpret it, what is the maximum time interval between that the drag racer initiating acceleration and its being hit by your car.
 
  • #3
What confuses me about this problem, is we don't know when "the last instant" is. It could be 1 metre before the car hits the dragster, could be when the d between the front of the car, and the tail of the dragster is 0 (at which point they'd ht, but I'd still call this the last instant).

I can't see any assumptions to be made. If we don't know when the dragster starts to accelerate, or the distance from the car to the dragster, I can't see how this can be done.

I could make an elaborate formula with a few constants chucked in, but I don't know if that's correct.
 
  • #4
wow nvm, i sort of somehow figured out that first one is = to v_0 over a, altho I am stull not sure what tmax is...

this is the next one tho:
Assuming that the dragster has started at the last instant possible (so your front bumper almost hits the rear of the dragster at t= t_max), find your distance from the dragster when he started. If you calculate positions on the way to this solution, choose coordinates so that the position of the drag car is 0 at t = 0. Remember that you are solving for a distance (which is a magnitude, and can never be negative), not a position (which can be negative).

but i still don't quite get tmax, cause i thought that WHEN they touched, the drag racer accelerated or something, so how does this make sense?
 
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  • #5
The problem asks for the 'maximum' time. That implies that the dragster guns it at the very instant the car is just about to hit it. You must calculate the time it takes for each to be touching each other, one accelerating, the other moving at constant speed. HINT: what can you say about the distance traveled by each when they touch?
 
  • #6
when they touch, the car has already traveled (i assume) v_o*tmax ?
but the dragster hasnt technically moved at all right?
 
  • #7
jcsp101 said:
when they touch, the car has already traveled (i assume) v_o*tmax ?
but the dragster hasnt technically moved at all right?
Oh, wait, sorry, i messed that up, forget my previous post. I agree with all that something is missing in this problem, and am also confused.
 
  • #8
yea eh, so now its this second problem whcih makes no sense since idk what Tmax is yet...
woo, got an hour an a half to try to figure it out.

gg, thanks anyway lol...
 
  • #9
jcsp101 said:
when they touch, the car has already traveled (i assume) v_o*tmax ?
but the dragster hasnt technically moved at all right?
Yes and no. I believe the problem is saying that after a certain amount of seconds have passed (t_max), the car can never hit the dragster, because it's speed will have equaled the speed of the car at that time, and will exceed it in the next instant, so the car can never catch it. So yourr answer for t_max = v_o/a appears correct, and the car will have traveled v_o*t_max. However, the dragster must already have moved a distance from his start equal to 1/2(a)t_max^2 during that period. A confusingly worded problem, if you ask me.
 
  • #10
Hey there! I have the same problem and was able to get the first part of t_max=v_0/a, however I am really confused on how to even approach the second question:Assuming that the dragster has started at the last instant possible (so your front bumper almost hits the rear of the dragster at ), find your distance from the dragster when he started. If you calculate positions on the way to this solution, choose coordinates so that the position of the drag car is 0 at . Remember that you are solving for a distance (which is a magnitude, and can never be negative), not a position (which can be negative). I'm not sure how to calculate the distance if it seems as if they will never touch because the dragster's speed will have to have equaled the car's speed at that instant of time. How am I supposed to solve for the distance D_start?
 

1. What is t_max in the Drag Racer Problem?

t_max is the time at which the drag racer reaches its maximum velocity before decelerating.

2. How is t_max calculated in the Drag Racer Problem?

t_max is calculated using the equation t_max = v_max / a, where v_max is the maximum velocity of the drag racer and a is the acceleration.

3. Why is t_max an important factor in understanding the Drag Racer Problem?

t_max is important because it helps determine the speed and acceleration of the drag racer, which are crucial in predicting its performance and making necessary adjustments.

4. Can t_max be affected by external factors?

Yes, t_max can be affected by external factors such as air resistance, friction, and track conditions. These factors can alter the drag racer's velocity and acceleration, thus changing the value of t_max.

5. How can understanding t_max help improve the performance of the drag racer?

By understanding t_max, adjustments can be made to optimize the drag racer's acceleration and speed, ultimately improving its overall performance. Additionally, knowing t_max can also aid in predicting the drag racer's performance in different conditions and making necessary modifications.

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