Projectile problem: with coefficient of kinetic friction?

In summary, Julia, who is driving at 15 m/s along a straight road, needs to drop a newspaper from a height of 1.00m so it slides along the shoulder and comes to rest in the customer's driveway. To find the horizontal distance before the driveway, she can use the equations delta y = Viy* delta t + 1/2 ay* delta t^2 and delta x = Vix * delta t, where the coefficient of kinetic friction between the newspaper and the ground is 0.40. The answer is 28.7m, which may seem high but is due to the low coefficient of friction and the lack of air resistance.
  • #1
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Homework Statement


Julia is delivering newspapers. Suppose she is driving at 15 m/s along a straight road and wants to drop a paper out the window from a height of 1.00m so it slides along the shoulder and comes to rest in the customer's driveway. At what horizontal distance before the driveway should she drop the paper? The coefficient of kinetic friction between the newspaper and the ground is 0.40. Ignore air resistance and assume no bouncing and rolling.

Homework Equations



delta y = Viy* delta t + 1/2 ay* delta t^2
delta x= Vix * detal t

The Attempt at a Solution


delta y = Viy* delta t + 1/2 ay* delta t^2
-1m=0 + 1/2(-9.8m/s^2)*delta t^2
==> delta t = sq. root of (-2* -1m/-9.8m/s^2) = 0.45s
delta x= Vix * detal t=15m/s * 0.45s = 6.78m

I am not sure what to do with the coefficient of kinetic friction between the newspaper and the ground? Please help! Or is it a trick to throw me off... the answer is just simply 6.78 m?
 
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  • #2
There are two stages of the motion. First the newspaper is a projectile, with horizontal initial velocity. In the second stage, it slides on the ground. Find the distance traveled in the horizontal direction as a projectile and then the distance traveled to full stop.

ehild
 
  • #3
ehild said:
There are two stages of the motion. First the newspaper is a projectile, with horizontal initial velocity. In the second stage, it slides on the ground. Find the distance traveled in the horizontal direction as a projectile and then the distance traveled to full stop.

ehild

Thank you so much.. NOw it makes sense why they thro that coefficient of K in there. soFriction the only force working against the newspaper at that phase?!

net force=ma = - Friction force = ma
- (coefficient k * m* g) = ma
a = -3.92
vf^2 = vi^2 + 2a delta x
x= 28.7m?

the distance from second stage is kinda high, it took 28.7m to reach full stop?
that's kinda crazy! Did I do it right? Thanks in advance!
 
  • #4
That 28.7 m is correct.
I think that the newspaper will not slide that long in reality, but that coefficient of friction is rather low for a rough surface as the road, and air resistance also acts on the newspaper. ehild
 
  • #5
ehild said:
That 28.7 m is correct.
I think that the newspaper will not slide that long in reality, but that coefficient of friction is rather low for a rough surface as the road, and air resistance also acts on the newspaper.


ehild

Thanks so much! You're so helpful! Have a wonderful day :)
 
  • #6
paxian said:
Thanks so much! You're so helpful! Have a wonderful day :)

Thank you:smile:

ehild
 

1. How do you calculate the coefficient of kinetic friction for a projectile problem?

The coefficient of kinetic friction can be calculated by dividing the force of friction by the normal force. The force of friction can be found by multiplying the coefficient of kinetic friction by the normal force. In a projectile problem, the normal force is equal to the weight of the object.

2. How does the coefficient of kinetic friction affect the trajectory of a projectile?

The coefficient of kinetic friction affects the trajectory of a projectile by reducing its speed and altering its direction. As the projectile moves, the force of friction acts in the opposite direction of its movement, slowing it down and changing its trajectory.

3. Can the coefficient of kinetic friction be negative in a projectile problem?

No, the coefficient of kinetic friction cannot be negative in a projectile problem. It is a measure of the resistance to motion between two surfaces, and it is always a positive value.

4. How does air resistance factor into a projectile problem with coefficient of kinetic friction?

Air resistance, also known as drag, is a form of friction that acts on a projectile as it moves through the air. It can affect the coefficient of kinetic friction by increasing the force of friction, thus reducing the speed and altering the trajectory of the projectile.

5. Are there any assumptions made when solving a projectile problem with coefficient of kinetic friction?

Yes, there are a few assumptions made when solving a projectile problem with coefficient of kinetic friction. Some of these include assuming a constant coefficient of friction, neglecting air resistance, and assuming a flat surface with no bumps or irregularities.

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