motion in opposite directions
DESCRIPTION
Motion in Opposite Directions. Objective: Solve word problems involving uniform motion. 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 - PowerPoint PPT PresentationTRANSCRIPT
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OBJECTIVE: SOLVE WORD
PROBLEMS INVOLVING UNIFORM MOTION
Motion in Opposite Directions
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Uniform Motion
Moving at a speed that is not changing.
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Distance = Rate x Time
D = RT (dirt)Rate x Time = Distance
50mph x 2hours = 100miles
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D/T = RDistance / Time = Rate
100miles / 2hours = 50mph
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Distance = Rate x Time
D/R = TDistance /Rate = Time
100miles / 50mph = 2hours
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Solving Word Problems
1. Draw a sketch 2. Identify Unknowns3. Assign Variable4. Make a Chart5. Write and solve an equation
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Equation for Motion in Opposite Directions
Add distance for both objects and set equal to the total distance apart.
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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.
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Start riding at 12pm & meet at 1:30pm
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Unknown
Jane and Brent’s speed.
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Variables
Let r = Jane’s rateLet r + 4 = Brent rate
Make a chart and use the information to label your diagram
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Chart
BIKE RIDINGBIKE RIDING RATERATE TIMETIME DISTANCEDISTANCE
JANEJANE
BRENTBRENT
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Equation
1.5 ( r + 4) + 1.5r = 60r = 18 Jane’s speedr + 4 = 22 Brent’s speed
Brent’s speed was 22km/h and Jane’s speed was 18 km/h
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Try ThisAt 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?
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2100 km
500 km
700 km
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500t + 700(t – 1) = 2100
TRAVELTRAVEL RATERATE TIMETIME DISTANCEDISTANCE
PLANEPLANE
JETJET
500
700
t
1t
500t
700( 1)t
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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