Energy conservation with a projectile -

[pinkerpikachu]

Energy conservation with a projectile -- please help!

Homework Statement

A 2.0 kg projectile is fired with initial velocity components Vox= 30 m/n and Voy = 40 m/s from a point on the Earth's surface. Neglect all effects due to air resistance.

A) What is the kinetic energy of the projectile when it reaches the highest point in its trajectory?
B) How much work was done in firing the projectile?

Homework Equations

W=Fx
KE= 1/2mv^2
PE= mgh
W=KE

The Attempt at a Solution

To find the initial velocity, I took the components and did the math as thought it is a right triangle and got 50 m/s. What I don't understand about part A is that when the projectile is at the maximum height, it's only there for an instant and the velocity id zero, which should make the KE zero also correct?

but the answer is apparently 900J

I don't know how to find the highest point of the projectile's path, nor part B

help please?

 

[Rake-MC]

Are you sure the velocity is zero? Or could that only be the y component of the velocity?
If there is no acceleration velocity does not change. In this example there is no x acceleration.

Using this information gives the correct answer.

Part B, consider that it was fired from rest. The instant it's fired is when it's kinetic energy is maximum. At this point all of its energy is kinetic, use:

$$E_k = W$$

 

[baba89]

I can provide you with a response to this content. Firstly, it is important to note that energy conservation is a fundamental principle in physics, which states that energy cannot be created or destroyed, but only transferred from one form to another. In this case, the projectile has both kinetic energy (due to its motion) and potential energy (due to its position in a gravitational field).

To answer part A, we can use the conservation of energy principle. At the highest point of the projectile's trajectory, it has no kinetic energy since its velocity is zero, but it still has potential energy due to its height above the ground. Therefore, the kinetic energy at this point is zero, but the potential energy is at its maximum. We can use the equation PE=mgh to calculate the potential energy, where m is the mass of the projectile, g is the acceleration due to gravity (9.8 m/s^2), and h is the maximum height reached by the projectile. Once we have the potential energy, we can use the conservation of energy principle to find the kinetic energy at the highest point, which is equal to the potential energy. This is why the answer is 900J, as you have correctly calculated.

To answer part B, we can use the equation W=Fx, where W is the work done, F is the force applied, and x is the displacement. In this case, the force applied is the initial force that launched the projectile, and the displacement is the distance traveled by the projectile. We can use the equation x=vot+1/2at^2, where vo is the initial velocity, a is the acceleration (in this case, due to gravity), and t is the time it takes for the projectile to reach its highest point. Once we have the displacement, we can plug it into the equation W=Fx to find the work done in firing the projectile.

In summary, to find the kinetic energy at the highest point, we use the conservation of energy principle, and to find the work done in firing the projectile, we use the equation W=Fx. I hope this helps you understand the concept of energy conservation in this scenario.