Bob is in his cruiser moving at 10 m/s down a straight highway. At t=0 s, he pas
ID: 1704424 • Letter: B
Question
Bob is in his cruiser moving at 10 m/s down a straight highway. At t=0 s, he passes a billboard; at the same moment, a distance 230 m ahead of him, he sees Alice merge onto the highway moving in the same direction as him. She is moving at 27 m/s but decelerating at 2.1 m/s^2. His speed and her acceleration remain constant throughout this problem.a) Where is Alice (as measured from the billboard) at t=7 seconds?
b) At what time will Alice attain the same speed as Bob?
c) Where will Bob overtake Alice (as measured from the billboard)?
Explanation / Answer
Given speed of Bob,vb = 10 m/s Distance between Bob and Alice,s = 230 m speed of Alice,va = 27 m/s Deceleration of Alice,a = -2.1 m/s^2 a)t = 7s s = va t +1/2 at^2 s = 27 m/s *7s + 1/2 (-2.1 m/s^2) (7s)^2 = 137.45 m b) Since vb = va + at 10 m/s = 27 m/s + (-2.1 m/s^2) * t t = 8.09 s c)If x be the distance travelled by Alice,then the distance travelled by Bob is 230+x in the same time t For Alice : x = 27t +1/2 (-2.1 m/s^2) * t^2 x = 27 t - 1.05 t^2 ---1 For Bob : t = 230+x /10 m/s ---2 substitute t from eq 2 in eq1 we get value of x where Bob overtaked Alice