Projectile MotionApparatuSTheoryDATA COLLECTIONOBSERVATIONSIntroductory Mechanics Experimental Laboratory1Projectile MotionGoals: Observe motion in two dimensions. Use simple measuring devices to make approximations. Understand the limits of precision in measurement.APPARATUS This experiment uses two glass tubes to launch a ball horizontally. Both tubes use grav-ity to get the ball rolling, and a straight section to launch the ball. A long tube will be used in part A to find the range of a ball. A short tube will be used in part B to plot the trajectory of the ball.In part A, the end of the long tube is situated at a height (h) above the ground. The ball comes out of the tube with an initial horizontal velocity (v0). As the ball flies through the air it will curve downward due to gravity and strike the floor some distance (d) away from the end of tube.In part B the ball curves downward and its path can be measured with a vertical board sided with carbon paper. The board can be place at various distances (x) away from the end of the tube. The impact of the ball on carbon paper leaves a mark that can be mea-sured at the end of the experiment. The sequence of carbon paper marks repesents the vertical position (y) of the ball at different points in flight.THEORY The ball comes out of either tube in the direction of the last section of the tube. This direction is purely in the horizontal direction at some initial velocity v0. This velocity can be measured by finding the time T that it takes to go between two points in the hori-zontal tube separetd by a distance (D). The velocity is then the (EQ 1)A projectile in the air is subject to an acceleration (a) downward due to Earth’s gravity. The acceleration only acts downward and has no effect on the horizontal motion. Since there is no initial vertical motion for the ball, the distance downward is given byv0DT⁄=2 Projectile Motion(EQ 2)where h is the initial height and g is the acceleration due to gravity, g = 9.8 m/s2.The time it takes to hit the ground is found by setting y equal to 0 (the ground) and solv-ing EQ 2 for t.(EQ 3)There is no acceleration in the horizontal direction so the forward distance covered when the ball hits the ground, called the range (R), is found by substituting the time from EQ 3 into an expression for distance: d = v0 t, or(EQ 4)A similar set of equations applies to the motion of a projectile before it reaches the ground. The vertical distance down from the starting point is y = gt2 and the horizontal distance is x = v0t. If these two equations are combined to eliminate t, then we get(EQ 5)This equation that relates two distances describes the trajectory of the projectile.DATA COLLECTION Part A - Long glass tube1. Measure the height of the long tube opening above the floor. This is the vertical dis-tance (h) that the ball will fall.2. Use a timer to determine how long it takes the ball to travel the distance between two marks separated by one meter while in the tube. Repeat your timing five times, recording each time, and take an average to use as time (T).3. Calculate the horizontal speed of the ball (v0) in the long level portion of the tube with D = 1 m using EQ 1.4. Use the height (h) and horizontal speed (v0) to predict how far out from the spot on the floor directly beneath the opening of the tube the ball will land using EQ 4. This is the range (R).5. Test your prediction by taping some carbon paper to the floor where you expect the ball to hit. Send the ball through the tube ten times letting it hit the paper each time to make a mark on the carbon paper.6. Measure the horizontal distance from the spot on the floor directly beneath the open-ing to the edge of the paper.7. Measure and record the distance of each mark on the paper from the edge of the paper and find an average.yy012---at2+ h12---gt2–==t2hg------=Rv02hg------=ygxv0-----2hgv02-------x2–==Projectile Motion 38. Add the average distance on the paper to the distance of the paper from the tube along the floor to get the measured range.Part B - Small glass tube1. Measure the height of the short tube opening above the table. This is the starting value of the vertical distance (h).2. Drop a small metal ball in the tube and watch its path after it leaves the tube; see how it curves downward. Do this a few times.3. Tape a strip of carbon paper with the white side out to the backstop. The top of the paper should be just above the point where the ball leaves the tube. Place the back-stop upright against the lower opening of the tube. Drop the ball five times, allowing it to hit the board.4. Move the backstop back 2 cm from the end of the tube. Drop the ball five times again. Try to hold the backstop vertical and as steady as possible during the five tri-als.5. Repeat step 4, moving the backstop back in 2 cm steps, until the backstop is so far away that the ball no longer hits it.6. Take the paper off of the backstop. Each set of five dots should be clearly separated from the others. Estimate by sight an average position from each group of dots, and mark it. 7. Next to each mark on the paper record the horizontal distance from the tube. This should begin at x = 0 and increase in steps of 2 cm.8. Determine the vertical position in cm of each average position marked on the paper. Use 0 cm for the mark at x = 0. Copy the numbers from the tape into a data table of x vs. y.9. Graph vertical distance vs horizontal distance. Notice that the graph has no time axis; only distance units (cm) are used. Your graph marks the trajectory of the ball.OBSERVATIONS Why did you take five measurements of the time with the long tube? How did the first time measurement compare with the average time?Compare your predicted range to the distance you just found experimentally. How good was your prediction? How close would your prediction be if you only used the first trial?What effects might account for the different positions of the marks?How does the graph of trajectory compare the curve you observed in step B.2? Describe any differences.How accurately were you able to measure the horizontal position in part B? How would this contribute to any differences in the trajectory?How does a graph of the trajectory differ from a graph of