Question

A goblin fires a 13.8-n flaming pumpkin from a cannon with a kinetic energy of 231.3 j. at the highest point in its trajectory, the pumpkin's kinetic energy is 164.0 j. the vertical height that the pumpkin reaches, relative to the launch point, is ________ m.

Answer 1

To determine the vertical height reached by the pumpkin, we can use the conservation of energy, assuming negligible air resistance. The vertical height that the pumpkin reaches is approximately 9.4 m.

Step-by-step explanation:

To determine the vertical height reached by the pumpkin, we can use the conservation of energy, assuming negligible air resistance. The initial kinetic energy (
`\(KE_{\text{initial}}\)`) is converted into gravitational potential energy (PE) at the highest point of the trajectory.

The formula for gravitational potential energy is PE = m · g · h, where:

- m is the mass of the pumpkin,

- g is the acceleration due to gravity (approximately 9.8 m/s² on Earth),

- h is the height.

The initial kinetic energy is equal to the gravitational potential energy at the highest point:

`\(KE_{\text{initial}}\)` = PE

`(1)/(2) m v_{\text{initial}}^2` = mgh

Canceling out the mass m from both sides, and solving for h:

h =
`\frac{v_{\text{initial}}^2}{2g}`

Plug in the values:

h =
`\frac{(13.8 \ \text{m/s})^2}{2 * 9.8 \ \text{m/s}^2}`

h ≈ 9.4 m

So, the vertical height that the pumpkin reaches is approximately 9.4 m.

Answer 2

To find the height reached by the flaming pumpkin, we can use the concept of conservation of energy and set up an equation for the kinetic energy at the highest point. By substituting the given values into the equation and solving for the height, we can determine the vertical height reached by the pumpkin.

Step-by-step explanation:

In order to find the height reached by the flaming pumpkin, we can use the concept of conservation of energy. At the highest point of the trajectory, the kinetic energy of the pumpkin is equal to its potential energy. We can set up the equation:

Kinetic energy at highest point = Potential energy at highest point

Using the given values, we have:

164.0 J = m * g * h

Where m is the mass of the pumpkin, g is the acceleration due to gravity, and h is the height reached by the pumpkin. Since the question doesn't provide the mass of the pumpkin, we can use the known kinetic energy and the given kinetic energy equation:

Kinetic energy = 0.5 * m * v^2

Substituting the values, we have:

164.0 J = 0.5 * m * (13.8 m/s)^2

Solving for m:

m = 164.0 J / (0.5 * (13.8 m/s)^2)

Once we find the mass of the pumpkin, we can substitute it into the equation for the potential energy:

164.0 J = m * 9.8 m/s^2 * h

Solving for h:

h = 164.0 J / (m * 9.8 m/s^2)

Substituting the value of m, we can find the height reached by the pumpkin.