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OBJECTIVE: SOLVE WORD PROBLEMS INVOLVING UNIFORM MOTION Motion in Opposite Directions.

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Presentation on theme: "OBJECTIVE: SOLVE WORD PROBLEMS INVOLVING UNIFORM MOTION Motion in Opposite Directions."— Presentation transcript:

1 OBJECTIVE: SOLVE WORD PROBLEMS INVOLVING UNIFORM MOTION Motion in Opposite Directions

2 Uniform Motion Moving at a speed that is not changing.

3 Distance = Rate x Time D = RT (dirt) Rate x Time = Distance 50mph x 2hours = 100miles

4 D/T = R Distance / Time = Rate 100miles / 2hours = 50mph

5 Distance = Rate x Time D/R = T Distance /Rate = Time 100miles / 50mph = 2hours

6 Solving Word Problems 1. Draw a sketch 2. Identify Unknowns 3. Assign Variable 4. Make a Chart 5. Write and solve an equation

7 Equation for Motion in Opposite Directions Add distance for both objects and set equal to the total distance apart.

8 Example Bike riders Brent and Jane started at noon from points 60 km apart and rode toward each other, meeting at 1:30pm. Brent’s speed was 4km/h greater than Jane’s speed. Find their speeds.

9 Start riding at 12pm & meet at 1:30pm

10 Unknown Jane and Brent’s speed.

11 Variables Let r = Jane’s rate Let r + 4 = Brent rate Make a chart and use the information to label your diagram

12 Chart BIKE RIDING RATETIMEDISTANCEJANE BRENT

13 Equation 1.5 ( r + 4) + 1.5r = 60 r = 18 Jane’s speed r + 4 = 22 Brent’s speed Brent’s speed was 22km/h and Jane’s speed was 18 km/h

14 Try This At noon a private plane left Austin for Los Angeles, 2100km away, flying at 500 km/h. One hour later a jet left Los Angeles for Austin at 700km/h. At what time did they pass each other?

15 2100 km 500 km 700 km

16 500t + 700(t – 1) = 2100 TRAVELRATETIMEDISTANCE PLANE JET

17 500t + 700(t – 1) = 2100 500t +700t – 700 = 2100 1200t – 700 = 2100 +700 =+700 1200t = 2800 1200t/1200 =2800/1200 T=2 and 400/1200 HRS or 2 and 1/3hrs is 2hrs 20min WHATS THE QUESTION Airplane took 2 hours and 20 min before meeting with Jet that took t – 1 =2hr 20 min – 1 = 1hr and 20 min Time is 12:00 + 2 hr and 20 min. They jet passed the plane at 2:20


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