Runner A is initially 6.2 Km west of a flagpole and is running with a constant velocity of 4.0 km/h due east. Runner B is initally 2.4 km east of the flagpole and is running with a constant velocity of 2.0 km/h due west. What will be the distance of the two runners from the flagpole when their paths cross?
2007-09-09 08:24:57 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Physics
S = VT and s = vT; where S = distance traveled for the V = 4 kph due E runner and s = distance for the v = 2.4 kph due W runner, both of whom run T time because they "cross" paths at the same place and time.
Let X = -6.2 km the starting point for the due E runner from the flagpole, which is at X = 0. Then x = 2.4 km on the other side of the flagpole for the due W runner.
Then X - VT = x - vT = d; where d is the place they meet at time T. Thus, X - x = VT - vT = (V - v)T and T = (X - x)/(V - v) which means the two runners will meet after T = 8.6/6 ~ 1.43 hr of running. For the faster runner, that means S = VT = 4*1.43 = 5.73 km from X = -6.2 km or d = X - VT = -.46 km just west of the flagpole.
As a check, the slower runner has to be there, too. So d = x - vT = 2.4 - 2*1.43 = -.46; so it looks as though there will be a collision.
2007-09-09 09:10:10 · answer #1 · answered by oldprof 7 · 0⤊ 0⤋
Let's assume that the flagpole is the dividing unit between positive an negative. Anything west, or traveling west, is negative and anything east or traveling east is positive.
Runner A's equation: 4t - 6.2
Runner B's equation: -2t + 2.4
Now, these are both position equations; when t is substituted, the equations reveal the position of the runner with respect to the pole.
With that in mind, let's find out when their positions are the same.
4t - 6.2 = -2t + 2.4, isolate the t from the numbers.
6t = 8.6, divide t's coefficient, 6.
t = 1.4 h, the time in which they cross.
Now, to determine their distance from the flagpole, substitute the time into one of the Runner's equations. It does not matter which; they are at the same location.
4(1.4) - 6.2 = -.6 km.
Remembering that anything west of the pole is negative, the Runners are at .6 km west of the flagpole.
2007-09-09 08:40:18 · answer #2 · answered by Matiego 3 · 0⤊ 0⤋
distance = velocity (time)
2007-09-09 08:34:43 · answer #3 · answered by 4 · 0⤊ 0⤋
tut tut! u shouldnt leave things till the last minute
2007-09-09 08:33:41 · answer #4 · answered by lil missy 2 · 0⤊ 2⤋