You ride your bike west at speed 8.0 m/s. Your friend, 400 m east of you, is rid

Question

You ride your bike west at speed 8.0 m/s. Your friend, 400 m east of you, is riding her bike west at speed 12 m/s. Complete the following steps to determine when your friend passes you. a. Sketch and Translate: Draw a sketch of the initial situation and choose a coordinate system to describe the motion of both bikes. Put all given information on the sketch; identify the unknown. b. Simplify and Diagram: Sketch a position-versus-time graph for each bike using the same coordinate axes. c. Represent Mathematically: Construct equations that describe the positions of each bicycle as a function of time relative to the chosen coordinate system. d. Solve and Evaluate: Use the equations to determine when the bicycles are at the same position. Does your result make intuitive sense? How do you know?

Explanation / Answer

using equation of time is t = d/v

dy = distance travelled by you

df = distance travelled by your friend

dy / vy = t = df / vf

d/8 = d + 400 / 12

12 d = 8 ( d + 400 )

12 d - 8 d = 3200

4 d = 3200

d = 3200 / 4

d = 800 m

t = d / v

t = 800 / 8

t = 100 sec

your friend and you pass is of 100 sec

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