OBJECTIVESOLVE PROBLEMS
INVOLVING UNIFORM MOTION
Uniform Motion Round Trip
Uniform Motion
Uniform motion is when an object moves without changing its speed.
Solving Word Problems
1. Draw a sketch 2. Identify unknowns3. Assign variable4. Make a chart5. Write and solve an equation
Equation for Motion Round Trip
Distance for object one equals the distance for object two.
Example
A ski lift carried Maria up a slope at the rate of 6 km/h, and she skied back down parallel to the lift at 34 km/h. The round trip took 30 min.
How long did she ski?
Draw a sketchDraw a Diagram
Assign Variables
Let t = Maria’s skiing time
Notice that 30 min = ½ hour
Make a ChartSKIINGSKIING RATERATE TIMETIME DISTANCEDISTANCE
UPUP
DOWNDOWN
30 t 6 30 t6
34tt34
34 6 30t t
34 180 6t t 6t 6t
40t 40
180
40
20 14 min 4 min40 2
t
Maria skied for 4.5 minutes downhill.She went up the lift for 30-4.5 or 25.5 minutes.How far did she ski? Oh ohSince km/h is in hours 4.5min=__hrsSmall to big divide. 4.5/60=3/40hours3/40hr x 34km/h =2 and 11/20km
Try This
Kathy hiked up a hill at 4 km/h and back down at 6km/h. His total hiking time was 3 hours.
How long did the trip up hill take him?
Make a ChartHIKINGHIKING RATERATE TIMETIME DISTANCEDISTANCE
UPUP
DOWNDOWN
4(3 )t4
6t6
3 t
t
6 4(3 )t t
4t 4t10 12t
10 12
10 10
t
6 11 1 12min
5 5t hr
10 12t
Kathy hiked down the hill for 1 hr 12 min.How long did the trip up take her? Since She went up the hill for 3 hrs - 1 hr 12min 1 hr 48 min minutes