Conservation of momentum - bullet/pendulum

[z2420]

Homework Statement

Bullet = 0.02 kg
pendulum block = 2 kg

bullet fired from (0m,0m) with velocity of (x m/s, 30 deg)
pendulum block located (30m, 30deg)
the maximum height reached by pendulum is 0.2 meter

what is the value of X

Homework Equations

I've tried several ways to approach this problem. the problem is the angle that it hits the bullet.

The Attempt at a Solution

If the angle was out of the problem, i get an answer of 199.98 m/s/s. i used mgh=1/2mv^2 to get the velocity final, then worked backwards to plug that into the conservation of momentum equation:

(0.02)(Vi) = (2.02)(1.98) = 199.98

this is about as far as i got without running into a wall. What i think is that the 199.98 is the X component, and using that I can solve for the resultant. But how?

 

[gneill]

Hi z2420, Welcome to Physics Forums.

It's not clear how this pendulum is supposed to look. How long is the pendulum string? Where does it pivot? Where is its "maximum height" measured from?

If the pendulum block is represented as a point mass at location 30m @30°, and the bullet is fired from the origin at 30°, how can the bullet ever strike the block if gravity is acting? (Trajectory will be parabolic, always below a slope 30° line from the origin). Is the bullet striking the block an elastic or inelastic collision?

If the pendulum string is just 0.1 meters long, any sufficiently speedy bullet will always make it reach its apex of 0.2m above its lowest point; The pendulum will go around in circles about its pivot!

Did the original problem statement come with a diagram?

 

[z2420]

there was no diagram and the problem stated was very unclear in itself

this is what i thought

the bullet in traveling upward at an angle of 30 degrees. Hitting the block and going inside. The block and bullet swing upwards at 0.2m. The length of the pendulum string is not stated. the pendulum looks like a string hanging 90 degrees from the top.

i think the 199.98 is the x trajectory. So under this (maybe incorrect) assumption, i calculated the y trajectory to get the resultant = 230.91 = initial velocity of bullet

think that's right?

 

[gneill]

I think that there are too many inconsistencies and unknown properties in the problem to make a valid judgment. Sorry.

 

[rwisz]

Thank you for sharing your approach to the problem. It seems like you have made some good progress in solving for the value of X, but as you mentioned, the angle of the bullet's trajectory can complicate the calculation. In order to fully solve for X, you may need to take into account the angle at which the bullet hits the pendulum block and how that affects the momentum transfer between the two objects. Additionally, you may want to consider the conservation of energy in this system as well. I suggest reviewing your calculations and equations to see if there are any steps or factors that you may have missed. Good luck with your problem solving!