We\'ve talked about motion that takes place in one dimension but it\'s more comm

Question

We've talked about motion that takes place in one dimension but it's more common for it to take place in two. For example, suppose you have one car heading north and another heading west toward the same intersection. We can describe motion in two dimensions using all the same formulas that we do motion in one dimension but using two coordinates. The diagram below shows this situation. The position in feet of the west bound car after t seconds is (600 - 42t, 0) and the position in feet of the north bound car is (0, -800 + 50t). To see what that means, in the table below the graph to get the location of each car at different times and graph those coordinates. I calculated their positions at t = 0 seconds as an example. Suppose I want to know the time at which the west bound car is 100 feet from the intersection. The coordinates of the point "100 feet from the intersection" on the west bound road is (100, 0). To find the time the car reaches that point, I can take the car's x-coordinate formula and set equal to the x-coordinate of that point: 100 = 600 - 400t - 500 = -400t t = -500/-400 = 1.25 seconds So the will be 100 feet away from the intersection after 1.25 seconds. At what time will the west bound car reach the intersection? At what time will the north bound car reach the intersection? Which car gets to the intersection first?

Explanation / Answer

1) coordinates of west bound car 600-42t

putting 600-42t = 0

gives t = 600/42 = 14.28 sec

2)coordinates of north bound car -800+50t

putting -800+50tt = 0

gives t = 800/50 = 16 sec

So west bound car reaches the intersection first.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.