# "Enhanced" Version

Once you have built and used the "basic" projectile spreadsheet, it is easy to "enhance" the basic projectile spreadsheet to:

• provide a graph of the trajectory (path) of the projectile.
• calculate the vector velocity of the projectile at any instant.
• calculate the direction of motion of the projectile at any instant.
• find a vectors x and y components from its magnitude (length) and direction.

Here's how:

1. By adding another column to the spreadsheet, it is easy to get an automatic graph of the trajectory (path) of the projectile. You have to move the vertical position column (D) next to the horizontal position, and then turn the values "upside down". To do this:
1. In cell G6, type the column heading "-y (m)".
2. In cell G7, type the formula "=-D7".
3. Use "Fill Down" to copy the formula in cell G7 to cells G8 through G32.
4. Use the mouse to select the values in columns F and G that you want to graph.
5. In the Options Menu, select "Make Chart".
6. In the dialog that appears, select "XY Line" and press OK. Neat, huh?
2. To calculate the vector velocity and direction of the projectile:
1. In cell H6, type the column heading "v (m/s).
2. The vector velocity can be calculated from the x-component and the y-component of the velocity using the Pythagorean Theorem. For cell H7, the formula is "=SQRT(B7*B7+E7*E7)".
3. Select cells H7 through H32, and use "Fill Down" to complete the column.
4. In cell I6, type the column heading "theta (deg)".
5. The tangent of the direction of the velocity vector equals the y-component divided by the x-component. Since the spreadsheet calculates trigonometric functions in radians, you have to convert the result to degrees. The formula for cell I7 is "=-180*ATAN2(E7,B7)/PI()".
6. Use "Fill Down" to complete the rest of the column.
3. Sometimes the starting velocity of a projectile is given in terms of its velocity and direction, and you need the x- and y-components of the velocity to enter in cells E7 and B7 respectively. You can have the spreadsheet calculate these values for you, as follows:
1. In cell F1, type the label "vel (m/s) =".
2. In cell F2, type the label "theta (deg) =".
3. In cell G1, type the velocity "100".
4. In cell G2, type the direction "45".
5. In cell H1, type the label "x vel (m/s) =".
6. In cell H2, type the label "y vel(m/s) =".
7. The x-component of the vector equals the magnitude of the vector times the cosine of the direction angle. Of course, you have to convert radians to degrees, too. The formula for cell I1 is therefore "=G1*COS(G2*PI()/180)".
8. The y-component of the vector equals the magnitude of the vector times the sine of the direction angle. Of course, you have to convert radians to degrees, too. The formula for cell I2 is therefore "=G1*SIN(G2*PI()/180)".

last update September 18, 2000 by JL Stanbrough