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Speedy Sue, driving at 30 m/s, enters a one-lane tunnel. She then observes a slow moving van 155 m ahead traveling 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.
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 traveled 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!
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 traveled 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!