How Fast Does Robin Hood's Arrow Propel the Sheriff's Hat?

  • Thread starter jenha14
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In summary, Robin Hood is confronted by the Sheriff of Nottingham in Sherwood Forest. After pulling out his bow and arrow, Robin shoots an arrow at the Sheriff's hat, which has a mass of 0.5 kg. The bow has a spring constant of 40 N/m and it takes 4N to pull it back 0.10 m. The arrow, with a mass of 0.20 kg, has an initial speed of 98 m/s before colliding with the hat at a final speed of 2.8 m/s. For part (B), it is a projectile motion problem and the arrow will take a certain amount of time to hit the ground, which can be calculated using a kinematic formula with
  • #1
jenha14
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Robin Hood is walking through Sherwood Forest when he comes upon the Sheriff of Nottingham. The Sheriff tells Robin Hood he is going to arrest him for numerous misdeeds. Robin pulls out his bow, loads an arrow, pulls the bow back 0.70 m, and shoots an arrow into the Sheriff's hat, knocking the hat with the arrow lodged in it off his head. The hat's mass is 0.5 kg. It takes 4N to pull Robin's bow back 0.10 m, and the arrow has a mass of 0.20 kg.
a) What is the speed of the hat with the arrow in it just after it is struck? Assume the arrow travels horizontally between Robin and the Sheriff and neglect air resistance.
b) If the Sheriff is 2.0 m high, how far behind him will his hat with the arrwo in it hit the ground?

For (a) I used F=kx and found it to be 40 N/m
 
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  • #2
jenha14 said:
For (a) I used F=kx and found it to be 40 N/m
OK, you found the value of k, the spring constant of the bow. Keep going. How much energy does the arrow have after it leaves the bow?
 
  • #3
I found the energy to be:

W = 1/2(k)(x)^2
 
  • #4
jenha14 said:
I found the energy to be:

W = 1/2(k)(x)^2
Good. Keep going. What's the arrow's speed just before it hits the hat? Then figure out the speed of "hat + arrow" after the the arrow hits the hat.

Hint: Treat the arrow sticking into the hat as an inelastic collision. What's conserved?
 
  • #5
I found that the speed of the arrow before the collision was:
KE = 1/2mv^2
9.8 J = 1/2(0.2 kg)(v)^2
v = 98 m/s

And used the equation:
m1v1i + m2v2i = (m1 + m2)vf
And found that the final velocity was 2.8 m/s

How do you start part (B)
 
  • #6
Part (B) is a projectile motion problem. You just found the initial velocity, which is horizontal. How long does it take before it hits the ground?
 
  • #7
Would I use F=ma to find the acceleration and then plug that into v=v0 + at to find the time?
 
  • #8
jenha14 said:
Would I use F=ma to find the acceleration and then plug that into v=v0 + at to find the time?
You'd be better off using a different formula, since you don't have the final velocity in the vertical direction. You have the distance, so find a kinematic formula with distance and time.

You shouldn't have to use F=ma to find the acceleration (though you could, of course). Since this is just a projectile, you should know the acceleration.
 

1. What is an "arrow problem"?

An "arrow problem" is a type of scientific problem that involves understanding and solving issues related to the flight or trajectory of an arrow. This type of problem is commonly encountered in fields such as physics, engineering, and ballistics.

2. What are the main factors that affect the flight of an arrow?

The main factors that affect the flight of an arrow include the weight and shape of the arrow, the force of the bow, the angle of the shot, and external factors such as wind and air resistance.

3. How can I calculate the trajectory of an arrow?

The trajectory of an arrow can be calculated using mathematical formulas that take into account the initial velocity, angle of the shot, and external forces such as gravity and air resistance. Specialized software programs are also available for more accurate calculations.

4. What are some common techniques for improving arrow flight?

Some common techniques for improving arrow flight include adjusting the weight and balance of the arrow, using a higher quality bow, and practicing proper shooting form and technique. Using arrow fletchings or vanes can also help stabilize the arrow during flight.

5. How can understanding arrow flight be applied in real-life situations?

Understanding arrow flight can be applied in various real-life situations, such as in sports like archery and hunting, as well as in military and law enforcement settings where precision and accuracy are crucial. It can also be useful in designing and testing projectiles for various purposes.

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