It is possible to predict the range of a projectile using kinematics equations (constant acceleration equations - i.e. neglecting air resistance). When doing so, the horizontal and vertical components must be treated separately. However, the kinematics equations can be combined to get this expression: (Range Equation) d = Y' sin 20. g We will call this the Range equation, where g is the acceleration due to gravity (9.8 m/s?), d is the range, or, total distance traveled horizontally (in meters), Vo is the initial muzzle velocity of your launcher, and O. is the initial launch angle. The range equation only applies for calculations involving a projectile being launched and landing at the same height (so that your Ay = 0). Remember: Vox would be the initial horizontal velocity, and Voy would be the initial vertical velocity, but v. is the magnitude of the total initial velocity vector (we could also call it muzzle speed). Draw a vector diagram in the space below, to show how you would obtain the magnitude if you were given Vox and Voy.

vector (we could also call it muzzle speed how you would obtain the magnitude if you were given Vox and Voy. Look at the equation given above. If your initial velocity is fixed (the launcher always fires with the same initial speed), and the acceleration due to gravity g doesn't change, what angle would give you maximum range? sin 8 1.0- 0.5 0.0- -0.5.01 180" 270' 360 -1.0 Hint: FIGURE 20.61 Graph of sine function between O and 360 degrees Does this agree with your findings from part A? 4.2.3 Firing and Landing at Different Levels Suppose you fire a projectile at an angle from the top of a cliff or some location where it lands at a lower level. Think about the angle which would give the greatest range. Do you predict that it will be the greater than, less than, or the same as the angle found for firing and landing at the same level (Activity 4.2.2)? Explain your prediction (vector diagrams and drawings of cliffs might help).Just as you did in Activity 4.2.2, we can experimentally determine the angle which produces the maximum range by plotting the range for various angles and determining the angle which produces the maximum of the resulting curve. In this activity, the data is filled in for you. Look at the data in the table and the completed graph. Launch Measured | Predicted Angle Range for Range (deg) Elevated (using Elevated vs. Same-Level Launch Launch "Range" 250.0 (cm) Equation) (cm) 200.0 A 15 180.0 52.2 150.0 20 189.0 67.2 Range (cm) 192.5 80.0 100. 30 192.5 90.5 50.0 35 189.5 98.2 40 184.7 102.9 0.0 0 10 20 30 40 50 60 70 80 45 177.8 104.5 Angle Launched (degrees) 50 170.5 102.9 In the graph above, the triangles represent the elevated launch ranges, and the 55 157.0 98.2 squares represent the predicted ranges using the range equation. Do the two data sets overlap? NO 60 141.5 90.5 65 123.0 80.0 70 96.2 67.2 75 72.4 52.2 From the data, what angle produces the maximum range for the elevated launch? 250 and 30 Is it smaller or larger than the angle that produces the maximum range for the same-level launch? 42elevated launch? Why does the range equation show a different curve from the curve that comes from the given data for the WOY 4.3 Analyzing Projectile Motion of a Trap-Jaw Ant 4.3.1 Introduction and disable prey. Surprisin