Answer:
1.40 N
Explanation:
The magnitude of the frictional force is given by:
where
is the coefficient of friction
N is the magnitude of the normal reaction
The coefficient of friction for this problem is . The magnitude of the normal reaction is equal to the combined weight of the boy and the sled, because the surface is horizontal, so
Therefore, the frictional force is
The speed of Matt is 10 mph.
Doug runs 2 miles an hour faster than Matt, so let Matt’s speed equal x miles per hour. Then Doug’s speed equals x + 2 miles per hour. Each lap is one-quarter of a mile, so Doug runs 1.5 miles in the time it takes Matt to run 1.25 miles.
Rate of Matt is x
Rate of Dough is (x + 2)
Time taken by Matt is 1.25/x
Time taken by Dough is 1.25/(x + 2)
Distance covered by Matt is 1.25
Distance covered by Dough is 1.5
Dough and Matt took the same amount of time from the time Doug started, so make an equation by setting the two times in the chart equal to each other, and then solve for x:
=
1.5x = 1.25(x + 2)
1.5x = 1.25x + 2.5
0.25x = 2.5
x = 10
So Matt ran at 10 miles per hour.
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