Question

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?

Answer 1

there will be collision

Step-by-step explanation:

`v_(s)` = speed of sue = 34 m/s

`v_(v)` = speed of van = 5.20 m/s

`v_(sv)` = speed of sue relative to van =
`v_(s) - v_(v)` = 34 - 5.20 = 28.8 m/s

`d_(s)` = stopping distance after brakes are applied

`D` = distance between sue and van = 160 m

`v_(f)` = final speed of sue = 0 m/s

`a` = acceleration = - 1.80 m/s²

Using the kinematics equation

`v_(f)^(2) = v_(o)^(2) + 2 a d_(s)`

`0^(2) = 28.8^(2) + 2 (1.80) d_(s)`

`d_(s) = 230.4` m

Since
`d_(s) < D`

hence there will be collision