Find Orig. Speed 3.0kg Mass After Frictionless Explosion

[ScullyX51]

Homework Statement

A 3.0 kg mass sliding on a frictionless surface explodes into 3 1.0kg masses. After the explosion the velocities of the three masses are: (1) 9.0 m/s north, (2) 4.0 m/s 30 degrees south of west, and (3) 4.0 m/s south of east. What is the original spped of the 3.0 kg mass?

Homework Equations

Pi=Pf
P=mv

The Attempt at a Solution

Pi=Pf
3v= (1)9+ (1)4+(1)4
I know this is wrong. I am confused about what to use for the magnitude and direction of these velocities. would it be 4tan(3) for both of them?

 

[tiny-tim]

A 3.0 kg mass sliding on a frictionless surface explodes into 3 1.0kg masses. After the explosion the velocities of the three masses are: (1) 9.0 m/s north, (2) 4.0 m/s 30 degrees south of west, and (3) 4.0 m/s south of east. What is the original spped of the 3.0 kg mass?
…
Pi=Pf
3v= (1)9+ (1)4+(1)4
I know this is wrong. I am confused about what to use for the magnitude and direction of these velocities. would it be 4tan(3) for both of them?

Hi ScullyX51!

Momentum is a vector, so you must use vector addition, not ordinary addition.

(since there are four vectors, a vector triangle won't be very much use , so: ) use x and y coordinates.

 

[thomate1]

I would approach this problem by first identifying the relevant equations and principles that can be applied. In this case, the conservation of momentum (Pi = Pf) and the equation P=mv are both applicable.

Next, I would carefully read and understand the given information. The problem states that a 3.0 kg mass explodes into three 1.0 kg masses, and the velocities of these masses after the explosion are given.

To find the original speed of the 3.0 kg mass, we can use the equation Pi=Pf and substitute the known values for the final momenta (Pf). However, we need to be careful with the direction of the velocities. In this case, the velocities are given in terms of their magnitudes and directions (north, south, and 30 degrees south of west).

To properly use these values in the equation, we need to convert them into their components in the x and y directions. For example, the velocity of 9.0 m/s north can be represented as (0,9) m/s in the x-y coordinate system. Similarly, the velocity of 4.0 m/s 30 degrees south of west can be represented as (-3.464, -2) m/s in the x-y coordinate system (using trigonometry to find the x and y components).

Once we have all the velocities in their x-y components, we can substitute them into the equation Pi=Pf and solve for the initial momentum (Pi). Then, using the equation P=mv, we can solve for the initial speed of the 3.0 kg mass.

In summary, as a scientist, I would approach this problem by carefully analyzing the given information, identifying the relevant equations and principles, and properly converting the given velocities into their x-y components to solve for the initial speed of the 3.0 kg mass.