Projectile Motion's relationship with Kinetic Energy and Potential Energy

In summary, the conversation discussed finding the initial velocity and range of a ball on a ramp setup on a tall table. The height Δy was measured and the kinetic energy and potential energy were set equal to each other to find the initial velocity of the x component. The formula for x component velocity was found to be √(2*g*hr). To find the time of flight, the formula y'-y= vy + 0.5gt^2 was used and the time was found to be √{ (2*∆y)/g }. The question then turned to finding the range of the object, with the suggested formula d= {v*cos(\Theta)}/g * [v*sin(\Theta)
  • #1
Whakataku
12
0
Imagine a ramp setup on top of a tall table. The height Δy is measured. To find the initial velocity at the instant the ball leaves the ramp, I set up the kinetic energy and potential energy equal to each other to find the initial velocity of the x component.

PE = KE
m*g*(hr) = 0.5*m*v^2
where hr is the height of the ramp and v is initial velocity (x-component)

solving for vx (x-component velocity), I got:
vx = √(2*g*hr)

To get the time for the object's time in flight:
y'-y= vy + 0.5gt^2
Δy= vy + 0.5gt^2, where Δy is the height from the ground to the ramp.
since θ= 0° I found t to be:
t = √{ (2*∆y)/g }

Now my question is how do I find the range of this object?
I started out with Δx = vx*t ; where vx is the initial x-component velocity... is that even right?
I'm hesitant to use it because written as Δx/t, it looks like an average velocity equation.
Furthermore, in Wikipedia I saw the equation

d= {v*cos([itex]\Theta[/itex])}/g * [v*sin([itex]\Theta[/itex]) + sqrt(v*sin([itex]\Theta[/itex])^2+2g*y)]

http://en.wikipedia.org/wiki/Range_of_a_projectile"
under uneven ground

but the problem is I don't have final velocity... or can I calculate the final velocity with the givens... if so how??

Could anyone please nudge me in the right direction to find Δx?

thanks.
 
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  • #2
I think I solved it... duh.

in the distance formula
d = v(initial)*t + 1/2*a*t^2.v(initial) and time is already attained and the the a acceleration is -9.81m/s^2
Correct me if I'm wrong.
 
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1. How does the height of a projectile affect its potential energy and kinetic energy?

The higher a projectile is launched, the greater its potential energy will be. This is because potential energy is directly proportional to the object's height above the ground. As the projectile falls towards the ground, its potential energy is converted into kinetic energy. Therefore, the higher the projectile is launched, the more kinetic energy it will have at its maximum height.

2. How does the mass of a projectile affect its kinetic energy?

The mass of a projectile does not directly affect its kinetic energy. According to the equation for kinetic energy, KE = 1/2mv^2, the mass of the object is already taken into account. However, a heavier projectile may have more potential energy due to its increased mass, which will then be converted into kinetic energy as it moves.

3. What happens to the kinetic energy of a projectile as it travels through the air?

As a projectile travels through the air, its kinetic energy remains constant. This is because, in the absence of external forces, the total energy of a system remains constant. As the projectile moves through the air, it may experience air resistance, which can decrease its kinetic energy. However, this decrease is negligible for most projectiles.

4. How does the angle of launch affect the potential energy and kinetic energy of a projectile?

The angle of launch affects the potential energy and kinetic energy of a projectile in two ways. First, the angle of launch determines the initial velocity of the projectile, which affects its kinetic energy. Second, the angle of launch also affects the height at which the projectile reaches its maximum height. The greater the angle, the higher the projectile will travel, resulting in more potential energy at its maximum height.

5. Can the potential energy of a projectile ever be greater than its kinetic energy?

Yes, the potential energy of a projectile can be greater than its kinetic energy. This can happen when the projectile is at its maximum height, where it has zero kinetic energy but still has potential energy due to its height above the ground. As the projectile falls, its potential energy decreases, and its kinetic energy increases until it reaches its maximum velocity at the bottom of its trajectory.

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