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

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Presentation transcript:

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

Uniform Motion Moving at a speed that is not changing.

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

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

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

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

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

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.

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

Unknown Jane and Brent’s speed.

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

Chart BIKE RIDING RATETIMEDISTANCEJANE BRENT

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

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?

2100 km 500 km 700 km

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

500t + 700(t – 1) = t +700t – 700 = t – 700 = = t = t/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: hr and 20 min. They jet passed the plane at 2:20