A 15.0-kg test rocket is fired vertically from Cape Canaveral. Its fuel gives it a kinetic energy of 1961 J by the time the rocket motor burns all the fuel. What additional height will the rocket rise?

m
- how do you organize this?
how do the J's fit in?

KE =PE = m•g•h

h = KE/m•g =1961/15•9.8 =13.34 m

Well, to answer your question, let me break it down for you in a way that makes sense.

First, we know that the rocket has a mass of 15.0 kg and a kinetic energy of 1961 J when the fuel is all burned. Now, remember that kinetic energy is the energy an object possesses due to its motion.

To find the additional height the rocket will rise, we can use the principle of conservation of energy. As the rocket rises, the potential energy increases while the kinetic energy decreases because its speed decreases.

Since at the end of the fuel burn the rocket has kinetic energy of 1961 J, the total energy at that point is 1961 J. We can assume that at this point the rocket has reached its maximum height, which means all its kinetic energy is converted to potential energy.

The potential energy of an object is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (about 9.8 m/s^2 on Earth), and h is the height.

So, to find the additional height the rocket will rise, we need to calculate h. We can rearrange the formula of potential energy to solve for h: h = PE / (mg)

Substituting the values, we get h = 1961 J / (15.0 kg * 9.8 m/s^2).

Now, simplifying the equation, we find h ≈ 13.5 meters.

Therefore, the additional height the rocket will rise is approximately 13.5 meters.

Remember, this is just a rough estimate, and I'm here to make you laugh, not for precise calculations. So, if you need a precise answer, consult a physics textbook or a rocket scientist! But for now, I hope this explanation brings a smile to your face!

To solve this problem, we need to use the principle of conservation of energy. The initial kinetic energy (K1) of the rocket is given as 1961 J. This energy comes from the fuel burning, so we can assume that all of the initial energy is converted into potential energy (PE) at the highest point of the rocket's trajectory.

The potential energy at the highest point is given by the equation PE = mgh, where m is the mass of the rocket, g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth), and h is the additional height the rocket will rise.

Since the rocket started with zero initial potential energy, we can equate the initial kinetic energy to the potential energy at the highest point:

K1 = PE

1961 J = mgh

Rearranging the equation:

h = 1961 J / (mg)

Substituting the given values:

m = 15.0 kg
g = 9.8 m/s^2

h = 1961 J / (15.0 kg * 9.8 m/s^2)

Calculating:

h ≈ 13.4 m

Therefore, the additional height the rocket will rise is approximately 13.4 meters.

To solve this problem, we need to use the principles of conservation of energy. The given information includes the mass of the rocket (15.0 kg) and the initial kinetic energy (1961 J) provided by the rocket fuel.

First, let's understand how to organize the information:

Given:
- Mass of the rocket (m) = 15.0 kg
- Initial kinetic energy (KE) = 1961 J

To find:
- Additional height the rocket will rise (Δh) in meters

Now, let's break down the information and explain how the units "J" fit in:

The unit "J" stands for joules, which is the unit of energy. In this case, the 1961 J represents the initial kinetic energy of the rocket. Kinetic energy is the energy an object possesses due to its motion. As the rocket motor burns all the fuel, it transfers energy to the rocket, enabling it to gain height.

Therefore, in this problem, the "J" represents the amount of energy provided by the rocket fuel, which is then converted into additional height for the rocket.

Now, let's move on to calculating the additional height the rocket will rise.