Projectile motion using conservation of energy problem

In summary, the conversation discusses using conservation of energy to find the maximum height reached by a projectile launched at an angle of 60 degrees and a speed of 40 m/s. The equation used is KEi + PEi = KEf + PEf, and the values for initial velocity, acceleration of gravity, initial y-position, final velocity, and final y-position are substituted to solve for the maximum height. The final answer is 61.2 meters.
  • #1
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Homework Statement


A projectile is launched with a speed of 40 m/s at an angle of 60 above the horizontal. Use conservation of energy to find the maximum height reached by the projectile during its flight.

Homework Equations


KEi + PEi = KEf + PEf (Initial kinetic energy + Initial potential energy of gravity = Final kinetic energy + final potential energy of gravity) rewritten as:
1/2mvi^2 + mgyi = 1/2 mvf^2 + mgyf
where:
vi = initial velocity
m = mass
g = acceleration of gravity
yi = initial y-position
vf = final velocity
yf = maximum height/final y-position

The Attempt at a Solution


I think I have this solved correctly, and I was wondering if anyone would be willing to confirm the answer I got.

These are the values I substitute:
vi = 40 m/s
g = 9.8 m/s2
yi = 0 m
vf = 40 cos(60) (my rational behind this is that at maximum height, the velocity is only in the positive x-direction)
yf = unknown solving for.

First, I cancel out the mass in the equation by dividing the entire equation by mass.

Next, I substitute values, ending up with:
1/2(40^2) = 1/2 (40 cos60)^2 + (9.8)yf
800 = 200 + 9.8yf
600 = 9.8yf
yf = 61.2 meters
 
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  • #2
It looks all right.

ehild
 

1. How is projectile motion related to conservation of energy?

Projectile motion is a type of motion in which an object is thrown or launched into the air, and moves along a curved path under the influence of gravity. This motion is related to conservation of energy because the total energy of the object, including its kinetic and potential energy, remains constant throughout the motion.

2. What is the equation for calculating the total energy in a projectile motion problem?

The equation for calculating the total energy in a projectile motion problem is E = KE + PE, where E represents total energy, KE represents kinetic energy, and PE represents potential energy. This equation is known as the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another.

3. How can we use conservation of energy to solve projectile motion problems?

We can use conservation of energy to solve projectile motion problems by setting the initial total energy of the object (at the point of launch) equal to the final total energy of the object (at the highest point of the trajectory). This allows us to solve for the unknown variables, such as the initial velocity or height of the object.

4. What are the key assumptions made in using conservation of energy for projectile motion?

There are several key assumptions made in using conservation of energy for projectile motion, including the assumption that there is no air resistance, no external forces acting on the object, and that the object is moving in a uniform gravitational field. These assumptions may not always hold true in real-world scenarios, but can provide a good approximation in many cases.

5. Can conservation of energy be applied to all types of projectile motion problems?

Yes, conservation of energy can be applied to all types of projectile motion problems, as long as the key assumptions hold true. This includes problems involving objects being thrown at an angle, launched from a height, or moving in a curved path due to a combination of forces. By using conservation of energy, we can accurately predict the motion of projectiles in a variety of scenarios.

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