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Speedy Sue, driving at 34.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 160 m ahead traveling at 5.20 m/s. Sue applies her brakes but can accelerate only at −1.80 m/s2 because the road is wet. Will there be a collision?

Respuesta :

Answer:

there will be collision

Explanation:

[tex]v_{s}[/tex] =  speed of sue = 34 m/s

[tex]v_{v}[/tex] = speed of van = 5.20 m/s

[tex]v_{sv}[/tex] = speed of sue relative to van  = [tex]v_{s} - v_{v}[/tex] = 34 - 5.20 = 28.8 m/s

[tex]d_{s}[/tex] = stopping distance after brakes are applied

[tex]D[/tex] = distance between sue and van = 160 m

[tex]v_{f}[/tex] = final speed of sue = 0 m/s

[tex]a[/tex] = acceleration = - 1.80 m/s²

Using the kinematics equation

[tex]v_{f}^{2} = v_{o}^{2} + 2 a d_{s}[/tex]

[tex]0^{2} = 28.8^{2} + 2 (1.80) d_{s}[/tex]

[tex]d_{s} = 230.4[/tex] m

Since  [tex]d_{s} < D[/tex]

hence there will be collision

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