Collision Prediction: Speedy Sue vs. Slow-Moving Van in a Wet Tunnel

[chr1zis]

here is the problem.. i keep getting yes for the first part and then around 163 for the second part. please help.

Speedy Sue, driving at 31.5 m/s, enters a one-lane tunnel. She then observes a slow-moving van 105 m ahead traveling in the same direction as her at 5.10 m/s. Sue applies her brakes but can decelerate only at because the road is wet. Will there be a collision?

yes or no?

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 0.00 for the time.

 

[cepheid]

Sue applies her brakes but can decelerate only at [...] because the road is wet. Will there be a collision?

I think a crucial piece of information is missing here. Also, please post what work you have done so far in attempting the problem

 

[chr1zis]

I think a crucial piece of information is missing here. Also, please post what work you have done so far in attempting the problem

Speedy Sue, driving at 31.5 m/s, enters a one-lane tunnel. She then observes a slow-moving van 105 m ahead traveling in the same direction as her at 5.10 m/s. Sue applies her brakes but can decelerate only at 1.85 m/s^2 because the road is wet. Will there be a collision?

yes or no?

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 0.00 for the time.

((i don't know if any of this is right, so please bear with me)) okay first i solved for t to get the time it took her to stop. -31.5=-1.85t.. t=17s. once i found that.. 17 x 5.10 = 86.7 .. then i took that and .. 86.7 x 105 = 191.7 .. then i got lost.. do i need to plug that into a kinematic equation or where do i go from here?

 

[cepheid]

So you approached the problem by calculating how long it would take Sue to come to a complete stop. That may be useful. But consider this...she does not need to come to a complete stop to avoid a collision. All she need to do is decelerate to a final velocity less than or equal to the van's (5.10m/s), and this deceleration has to occur quickly enough that she achieves this final velocity before reaching the van. But that's really hard to calculate just like that...after all, her velocity is changing continously. I'd recommend using the given initial conditions and the kinematic relations to find the positions of each vehicle as a function of time: x(t) Then, if at some time t, the positions of the two vehicles are the same, they have collided. In other words, you want to see if those two functions intersect at any point.