# Newton's laws questions

Right well there is this question which I am stuck on and could do with some help with! Thanks!

A runner decelerates as he runs into a windy exposed area, from a speed of 4 m/s to 2 m/s in 8 seconds. His mass is 60 kg. Assuming he also experiences a frictional force of 3 N, find the size of the force exerted by the wind on the runner.

I have found the resultant force to be 15N but to calculate the wind I'm sure it cannot just be 12N because the force pushing the man forwards has to be taken into account as well. I'm all rather confused about it!

There is also this question which I am a bit stuck with:

A stone of mass 50g is dropped into some liquid and falls vertically through it with an acceleration of 5.8 m/s^2. Find the force of resistance acting on the stone.

Many thanks!

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HallsofIvy
Homework Helper
What force "pushing him forward"?

The one ambiguous point in this problem is the statement
"Assuming he also experiences a frictional force of 3 Newtons" Since there is also a reference to the wind force, I take that that is the friction of the ground on the runner. It is, I agree, ambiguous whether this force is positive or negative (whether the runner is trying to accelerat or not). Since the runner slows down, I think it is most reasonable to assert that this is also negative.

Slowing from 4 m/s to 2 m/s in 8 seconds means an acceleration of
-2/8= -0.25 m/s2. F= ma so F= (60)(-0.25)= -15 N as you calculated. Assuming that the friction force is negative, the force of the wind is -12N.

For the second problem, a stone of mass 50g (so 0.05 kg) would have acceleration -9.8 if it were falling freely. Since it is falling with acceleration -5.8 m/s2, there must be a retarding force of (0.05)(-5.8-(-9.8))= 0.05(4.1)= 0.205 N. (positive since it is upward.)