Speedy Sue, driving at 30.0 m/s, enters a one-lane tunnel. She then observes a s

Question

Speedy Sue, driving at 30.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van155 m ahead travelling at 5.00 m/s. Sue applies her brakes but can accelerate only at 2.20m/s^2 because the road is wet. Will there be a collision? If yes, determine how far into the tunnel and atwhat time the collision occurs. If no, determine the distance of closest approach between Sue’s car and the van.

I'm confused on this. I found a similar problembut the acceleration was a negative value. I keep ending up with a negative square root and don't think I'm doing this right. Please show all work so I can understand! Thanks

Olivia

Explanation / Answer

The distance travelled before stopping

x = v^2 / 2 x acc = 30^2 / 2 x 2.2 = 204 mtrs.

So, there will be a collison.

The distance covered by van and car = 155 m

So, let t be the time taken to travel. Then,

distance travelled by car = vt - .5 x acc x t^2 = 30 t - 1.1t ^2 = distance travelled by van = 5t

So, 1.1t^2 - 25t = 0

So, t = 0 or t = 25/1.1 = 17.86 secs

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