# Can we use conservation of energy law to find final velocity

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1. Nov 24, 2014

### justduy

1. The problem statement, all variables and given/known data
It's a simple problem, you kick a ball with an initial velocity of 5.4 m/s, the angle is 30 degrees. So the question is when does it land on the ground?

So I thought that I could find final velocity so that I can use V = V(initial) + acceleration * time. My question is, can you use the law of conservation of mechanical energy (Energy Total (i) = Energy Total (ii)) to find final velocity? Then final velocity would be the same as initial velocity? Since the potential energy in both positions would be 0 due to 0 height?

As I am writing this I realized that if I used the position of max height instead of initial position, I would get a different answer? Why?

EDIT: The maximum height is 0.375m

2. Nov 24, 2014

### Simon Bridge

You forgot about the kinetic energy at the max height?

3. Nov 24, 2014

### tzar1990

I would actually imagine this is just a kinematics question - if you're only dealing with when it lands on the ground, it's easy to calculate the velocity up. And since you know initial velocity in the relevant direction, acceleration due to gravity, and final displacement (0), it should be fairly easy to calculate the time taken.

4. Nov 24, 2014

### Staff: Mentor

Velocity is a vector whereas kinetic and potential energies are scalars. So what conservation of energy can give you is speed (also a scalar). So yes, thanks to conservation of energy you can state that the initial speed of the ball is the same as its speed upon landing.

However, you can also break down the motion of the ball into separate horizontal and vertical components. It so happens that energy is conserved in those separate motions, too. So if you know the vertical component of the velocity at launch, then the vertical component of the velocity upon landing will have the same magnitude (but not the same sign!).

You should be able to write the kinematic equation for the final value of the vertical velocity component given the initial velocity component and solve for the time.

5. Nov 25, 2014

### lep11

I personally would treat it like a projectile motion problem.

6. Nov 25, 2014

### Simon Bridge

One way of treating a projectile motion problem is via conservation of energy.

7. Nov 26, 2014

### lep11

I should have been more specific. I personally like to solve problems like this with a little vector algebra and kinematics equations but it is up to him/her which method he/she chooses.