speedy sue, driving at 30.0 m/s, enters a one-lane tunnel. she then observes a slow-moving van 155m ahead traveling at 5.00m/s. Sue applies her brakes but can accelerate only at -2.00m/s because the road is wet. Will there be a collision? If yes, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of closet approach between Sue's car and the van.
2007-08-28 13:19:39 · 1 answers · asked by bob b 2 in Science & Mathematics ➔ Physics
the equation of motion for sue while braking is
sue(t)=30.0*t-.5*2.00*t^2
or
sue(t)=30.0*t-t^2
assuming the van maintains constant speed, the equation of motion of the van in sue's coordinate system is
van(t)=155+5.00*t
to determine if collision occurs, check to see if
sue(t)=van(t) for a real, positive t
30.0*t-t^2=155+5.00*t
0=t^2-25*t+155
It has two real, positive roots. The smaller is relevant at 11.382 seconds.
That places both vehicles 212 meters inside the tunnel at the same moment = collision
j
2007-08-29 07:28:20 · answer #1 · answered by odu83 7 · 0⤊ 0⤋