# Calculating final speed using momentum

• ilovedeathcab
In summary, to calculate the final speed of the girl after jumping onto the skateboard, we can use the law of conservation of momentum, which states that the total momentum before the interaction is equal to the total momentum after the interaction. By setting up the equation m1v1i + m2v2i = m1v1f + m2v2f and plugging in the known values (m1=73.8 kg, m2=3.4 kg, v1i=4 m/s, v2i=0 m/s), we can solve for the final velocity of the girl (v1f), which will be the same as the final velocity of the skateboard (v2f).
ilovedeathcab
calculating final speed using momentum [solved]

1. A 73.8 kg girl runs at 4 m/s and jumps onto a 3.4 kg stationary skateboard. Ignore friction and calculate the final speed of the girl.

* Answers will be accepted if they are within 0.2 of the correct answer.
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2. I understood that this uses the law of conservation of momentum, but couldn't get past this basic equation without getting it wrong.
m1v1i + m2v2i = m1v1f + m2v2f

Assuming object 1 is the girl, and object 2 is the skateboard, v2i would equal 0 (stationary skateboard), v1i would equal 4m/s (girl), and you would plug in the masses (m1=73.8, m2=3.4kg). I'm not sure what to put in for v2f, becuse it doesn't specify in the problem the final velocity of the skateboard. I'm pretty sure I'm missing the big picture.

Last edited:
The girl and the skateboard move with the same final velocity.

The final speed of the girl can be calculated using the law of conservation of momentum, which states that the total momentum of a system remains constant in the absence of external forces. In this case, the initial momentum of the girl (m1v1i) must equal the final momentum of the girl and skateboard together (m1v1f + m2v2f). Therefore, we can set up the following equation:

m1v1i = m1v1f + m2v2f

Substituting in the given values, we get:

73.8kg * 4m/s = 73.8kg * v1f + 3.4kg * v2f

Rearranging the equation to solve for v1f (the final speed of the girl), we get:

v1f = (73.8kg * 4m/s - 3.4kg * v2f) / 73.8kg

Now, we need to find the final velocity of the skateboard (v2f) in order to solve for v1f. Since the skateboard and girl are now moving together as one system, their final momentum will be equal to the initial momentum of the girl (m1v1i). Therefore, we can set up another equation:

m1v1i = m1v1f + m2v2f

Substituting in the values, we get:

73.8kg * 4m/s = 73.8kg * v1f + 3.4kg * v2f

Since we already know the value of v1f, we can plug that in and solve for v2f:

73.8kg * 4m/s = 73.8kg * ((73.8kg * 4m/s - 3.4kg * v2f) / 73.8kg) + 3.4kg * v2f

Simplifying and solving for v2f, we get:

v2f = 0.98m/s

Now that we have both v1f and v2f, we can plug them back into the original equation to solve for the final speed of the girl:

v1f = (73.8kg * 4m/s - 3.4kg * 0.98m/s) / 73.8kg = 3.95

## 1. How is momentum calculated?

Momentum is calculated by multiplying an object's mass by its velocity. The equation for momentum is p = m * v, where p represents momentum, m represents mass, and v represents velocity. Momentum is measured in units of kilogram-meters per second (kg*m/s).

## 2. What is the formula for calculating final speed using momentum?

The formula for calculating final speed using momentum is vf = p/m, where vf represents final speed, p represents momentum, and m represents mass. This formula is derived from the equation for momentum, p = m * v, by solving for v.

## 3. How do you use the principle of conservation of momentum to calculate final speed?

The principle of conservation of momentum states that in a closed system, the total momentum remains constant. This means that the initial momentum of an object before a collision or interaction is equal to the final momentum of the object after the collision or interaction. By setting the initial momentum equal to the final momentum and solving for the final speed, we can use the principle of conservation of momentum to calculate final speed.

## 4. Can final speed be negative when calculating using momentum?

Yes, final speed can be negative when calculating using momentum. In physics, velocity is a vector quantity that includes direction. A negative final speed indicates that the object is moving in the opposite direction of its initial velocity. This can occur when an object experiences a change in direction during a collision or interaction, causing its final velocity to be in the opposite direction of its initial velocity.

## 5. How can calculating final speed using momentum be applied in real-world situations?

Calculating final speed using momentum can be applied in various real-world situations, such as car crashes, sports collisions, and even rocket launches. By understanding the principles of momentum and conservation of momentum, scientists and engineers can predict the outcomes of these interactions and design safety measures to reduce the impact of collisions. Additionally, calculating final speed can also be used to determine the efficiency of propulsion systems, such as in rocket engines.

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