Projectile Motion/ Air Resistance Question

In summary: So the ratio is ##1.69/1##, or 0.69, which is the same as multiplying by 0.69. Does that make sense?In summary, for the first question, we are given the mass, angle, and height of an arrow fired at a target. Using the conservation of energy formula, we can solve for the initial speed of the arrow, taking into account the 10% loss of energy due to air resistance. For the second question, we are given the final speeds and heights of two objects dropped from a cliff, with one object being 30% faster than the other. To find the difference in kinetic energy, we can use the formula for kinetic energy and take the ratio of the kinetic
  • #1
VanessaN
12
1
I actually have 2 questions that I am getting stuck on around the same point..

Question 1) An arrow with a mass of 80g is fired at an angle of 30 degrees to the horizontal. It strikes a target located 5 m above the firing point and impacts the target traveling at a speed of 20 meters/sec. If 10% of the initial energy of the arrow is lost to air resistance, what was the initial speed of the arrow?

My attempt at the problem: Energy final= Kf + Uf = 1/2*m*vf^2 + m*g*hf

Energy initial= Ki + Ui = 1/2*m*vi^2 + m*g*hi (but since initial height is 0)= 1/2*m*vi^2
Wnonconservative= Ei- Ef= 1/2*m*vi^2 -(1/2*m*vf^2 + m*g*hf)And since 10% of the initial energy is lost,
Wnonconservative= 0.1* Ei= 0.1* (1/2*m*vi^2)This next step is where I am getting confused, in solving for the initial speed:Wnonconservative= 1/2*m*vi^2 -(1/2*m*vf^2 + m*g*hf)so0.1* (1/2*m*vi^2)= 1/2*m*vi^2 -(1/2*m*vf^2 + m*g*hf)
The solution in the book is 23.5 m/s, but I don't know how to get it from here. Please help!

Question 2) Two different objects are dropped from rest off of a 50 m tall cliff. One lands going 30% faster than the other, and the two objects have the same mass. How much more kinetic energy does one object have at the landing than the other?
My attempt at the problem:
Vi=0

Vfinal, faster object= 1.3

Vfinal, slower object=1

initial height=50 m

final height= 0

mass,m
So the difference in kinetic energy is:

1/2 *m *(1.3v)^2 - 1/2 *m *v^2= ?
The answer is 69% more kinetic energy for the faster rock, but I'm having trouble finding out how to get that from here. Any help is very much appreciated! Thanks!
 
Physics news on Phys.org
  • #2
VanessaN said:
The solution in the book is 23.5 m/s, but I don't know how to get it from here. Please help
You have all of the values except vi. Simply solve for vi and insert the values in the resulting equation.

VanessaN said:
The answer is 69% more kinetic energy for the faster rock, but I'm having trouble finding out how to get that from here.
You are looking for the ratio of the kinetic energies, not their difference.
 
  • Like
Likes VanessaN
  • #3
Thank you! I got the first question, but for the second question, I'm not sure if I'm using the correct method to get the answer..

1/2* m * (1.3v)^2 - 1/2* m * v^2 = (supposed to equal) 0.69 * 1/2 * m * v^2, but how do I get that...

1/2* m * 1.69* v^2 - 1/2* m* v^2
= 0.845* m*v^2 - 0.5 * m* v^2
= 0.345 m*v^2 ... which if you multiply by 2 you get 0.69, so
= 0.69 * 1/2 * m * v^2

There we go! I think I got it now thank you :)

Is there any easier way to solve then doing all of that? Because it'd be tricky to remember to have to multiply the 0.345 * 2 to get 0.69 * 1/2 * m * v^2...but I guess I'll just have to remember to solve to get 1/2 * m * v^2 since we are solving for kinetic energy
 
Last edited:
  • #4
VanessaN said:
Is there any easier way to solve then doing all of that?

Yes, taking the ratio of the kinetic energies. Everything apart from ##1.3^2 = 1.69## will cancel.
 
  • Like
Likes VanessaN

FAQ: Projectile Motion/ Air Resistance Question

1. What is projectile motion?

Projectile motion is the motion of an object through the air, subject to only the force of gravity. It is a type of motion that is commonly seen in sports, such as throwing a ball or shooting a basketball.

2. How does air resistance affect projectile motion?

Air resistance, also known as drag, is a force that opposes the motion of an object through the air. It can change the trajectory and speed of a projectile, making it deviate from its expected path. The larger the surface area of the object, the greater the air resistance will be.

3. Can air resistance be ignored in projectile motion calculations?

No, air resistance cannot be completely ignored in projectile motion calculations. While it can be neglected in some cases, such as when the object is small and moving at low speeds, it becomes increasingly significant as the object's size and speed increase.

4. How can you calculate the effect of air resistance on a projectile?

The effect of air resistance on a projectile can be calculated using the equations of motion, which take into account the force of gravity and the force of air resistance. Computer simulations can also be used to accurately model the trajectory of a projectile in the presence of air resistance.

5. How can air resistance be reduced in projectile motion?

Air resistance can be reduced in projectile motion by making the object more aerodynamic, or streamlined. This means reducing its surface area and minimizing any protruding or irregular parts. Additionally, increasing the speed of the object can also help to reduce the impact of air resistance.

Back
Top