How to find the maximum angle of a pendulum after a mass collides with it

[SMilo]

Homework Statement

A 10g ball is fired at 6 m/s into a 280g pendulum. What maximum angle will the pendulum swing to if the effective radius of the pendulum is 28cm?

Homework Equations

How to find theta?

The Attempt at a Solution

I converted 28cm to 0.28m; 10g to 0.010kg; and 280g to 0.280kg. I used the equation 1/2mv^2 = mgh to find h to be 1.835. Then I plugged it into inverse cos but get a domain error, like so cos^-1(1.835/0.28).

 

[scottdave]

You know that there are 2 different masses? One mass for the bullet, and one for the combined bullet+pendulum.

 

[haruspex]

You need to break the process into two phases: the collision and the subsequent motion.
It does not say so, but you should assume the masses stick together, or at least, have the same velocities just after the collision. Otherwise you do not have enough information.

 

[CWatters]

Your value for h is more than twice the radius of the pendulum.

 

[neilparker62]

An observation arising from alternate method:

After the "collide and coalesce" collision , there is virtually no energy left to lift the combined mass. Energy loss calculated as 1/2 μ Δv^2 where:

μ=m1 * m2 / (m1 + m2) and Δv is the relative velocity of colliding objects - in this case 6m/s.

However it's not really clear from the question whether this is an elastic or inelastic collision. My reading of "fired into" is that it's a perfectly inelastic collision.