Interactive Lecture Demonstration 4 – Howitzer II

The Howitzer returns – this time aimed at an upward launch angle of 30 degrees above horizontal. Also, rather than hitting the floor, the cannonball will be launched from one end of a table and will hit the tabletop somewhere at the other end of the table.

The goal of this activity is to predict, then measure, the maximum height of the cannonball, its time of flight, and its "range (defined to be the horizontal displacement of a projectile whose vertical displacement is zero).

A. Finding the maximum height

1. First, follow the usual procedure for a DVAT problem in two dimensions by drawing your diagram, defining your initial and final locations, and writing down 5 DVAT variables that you already know for this problem. You will need to make a velocity triangle – show your triangle and show how you use it to find your DVAT knowns.

2. You should be able to easily use your given variables to solve for the max height. Do that now. Do not sub in numbers until the last step ! Put units on all numbers !

B. Finding the time of flight

Use the given information to find the total time that the cannonball is in the air. Make sure that you choose the final location appropriately for this part.

C. Finding the range

So far, we have only used the vertical DVAT variables – we have really been doing only one-dimensional problems here ! Now we will need to use the second dimension to find the cannonball's horizontal displacement when its vertical displacement is zero (i.e. the range of the cannonball). Use the appropriate horizontal DVAT equation now to find the range:

D. Comparison of measurements with predictions

Estimate the maximum height, time of flight and range of an actual launched cannonball. How closely do they match the predictions of our DVAT theory ? What are some possible reasons (other than the inevitable uncertainties in making the measurements) for discrepancies between theory and experiment here ?