You and a friend are measuring a field for an ecology experiment. You walk due e

Question

You and a friend are measuring a field for an ecology experiment. You walk due east at a speed of 0.9 m/s and your friend moves in a direction 25o east of north at a speed of 1.2 m/s. Both of you walk for 90 seconds when you simultaneously stop. At the end of the walk, how far from your friend are you?

Give your answer in meters, but do not include the units in your answer.

You should provide your answer to at least three significant figures to avoid being counted incorrect due to rounding. You will not be graded on the number of significant figures.

Explanation / Answer

Call east +x and north +y.

Suppose you both start at the origin.

After 90s your

x coordinate is 0.9*90 = 81 m

y coordinate is 0

Your friend has:

x component of velocity = 1.2*sin(25) = 0.507m/s

y component of velocity = 1.2*cos(25) = 1.087m/s

After 90s your friend's

x coordinate is 90*0.507 = 45.63 m

y coordinate is 90*1.087 = 97.83 m

now we have two point (81, 0) and (45.63, 97.83).

distance between you and your friend = distance between two point (81, 0) and (45.63, 97.83)

= sqrt[(81 - 45.63)^2 + (97.83 - 0)^2] = 104.03 m = 104 m (approx)

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