Calculating the speed of the baseball

[aeromat]

Homework Statement

You and some classmates read that the record for the speed of a pitched baseball is 46.0m/s. You want to know how fast your school's star baseball pitcher could throw.

You made a pendulum with a rope and a small box lined with a thick layer of soft clay, so that the baseball would stick to the inside of the box upon collision. You drew a large protractor on a piece of paper and placed it at the top, so that one student could read the max. angle of the rope when the pendulum swung up.

The rope was 0.955m long, the box with clay had a mass of 5.64kg, and the baseball had a mass of 0.350kg. Your star pitcher pitched a fastball into the box and the student reading the angle recorded a value of 20.0° from the resting, vertical position. How fast did your star pitcher pitch the ball?

Homework Equations

Conservation of Momentum
Conservation of Energy
Work

The Attempt at a Solution

I am not sure what to do here, because we are not given height to work with, and I am unaware with how the conservation of energy will work with this.. I just need a few pointers to get me started..

 

[gneill]

Assuming that the pendulum rope remains taut, the deflection angle should allow you to determine the change in height of the bob (box + baseball). It's basic trigonometry.

 

[aeromat]

How? I can see the triangle that can be formed from this;
0.955m hypothenuse
0.955sin20°
0.955cos20°

I don't know how to carry on the problem from there, because I am not sure how to get the height. The height isn't part of the triangle, because that is beneath and the triangle forms upward..

 

[gneill]

The rope doesn't change length. When it is hanging straight down it is length L from the pivot point. When the rope is at its highest angle, how far below the pivot point is it? Whats the height difference?