Speedy Sue, driving at 30 m/s, enters a one-lane tunnel. She then observes a slow moving van 155 m ahead travelling at 5 m/s. She applies her brakes but can accelerate only at -2.0 m/s^2 because the road is wet. Will there be a collision? If yes, determine how far into the tunnel and what time the collision occurs. If no, determine the distance of closest approach between sues car and the van.(adsbygoogle = window.adsbygoogle || []).push({});

here's my greatest guess....

i'm going to assume they collide...(if i can do that)

S----------- 155 m -----------V--------x---------C

where...

S = sues starting position

V = the vans starting position

x = the distance travelled by the van

c = collision

SUE:

d = vt + 1/2at^{2}

155+y = 30t - t^{2}

y = 30t - t^{2} - 155

VAN:

d = vt + 1/2at^{2}

y = 5t

therefore...

30t - t^{2} - 155 = 5t

t^{2} - 25t + 155 = 0

using the quadratic formula, i got

t = 13.62 and t = 11.38 seconds (approx.)

now which one do i accept? am i doing this right or the smartest way? thanks!

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# Homework Help: Will there be a collision?

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