Experiment M4: Projectile MotionIn this experiment you will study the path of an object as it movesin two dimensions under the influence of gravity.You will do this by repeatedly launching a ball and intercepting it at different points in the path that it travels.Consider the object in the figure at left.It is moving in two dimensions with velocity and acceleration .The position is given by:2002atrrvt avrThe velocity is given by:0vv at The parameters r, v and a in these equations are vectors and as such may be resolved into orthogonal x and y components.In the x direction, since a = 0, we have:0xxvt0xxvvandIn the y direction, since a = -g, we have:0yyvvgt202ygtyvt00cosxvvwhereandwhere00sinyvvCombining these equations and eliminating t yields y as afunction of x:2220tan2cosgyxxvIf we let x = D and y = -h as shown in the figure, then h as a functionof D becomes:2220tan2cosghD Dv 220tan2coshgDDvIf we divide both sides of this equation by D, we have:Comparing this with the slope-intercept form of a lineysxb220 tan2coshyDxDgsbvYou will measure h for a series of values of D and use thesedata to determine the launch speed v0and the launch angle .V-1 and V-2V-1: Use the plumb-bob to determine point B from the figure ofthe apparatus. Measure and record height S from the figure.V-2: Launch the ball once to determine point F from the figure ofthe apparatus. Place a line of masking tape on the floor connecting B and F. Place the piece of carpet at point F and practice launching the ball until you can consistently hit the same point.V-3Place a strip of pressure sensitive paper (two sheets-white facing out and yellow underneath. Mark H on the paper as shown. Each member should measure as shown using the plumb-bob.V-4Place the vertical board such that D = 25-30 cm and record D. The paper side of the board should be perpendicular to the path of the ball and centered on the tape line connecting points B and F. Launch the ball 5 times.You will determine h five times at each value of D. You should have a total of 8 values of D, each separated by 5-10 cm.VI-1 and VI-2 of the reportVI-1: Tabulate h, D and h/D. It is probably best to tabulate the data as shown, where D1is the first value of D, h1-1is the first value of h atD1, h1-2is the second value of h at D1 etc.This will make it easier to plot your data. D (cm) h (cm) h/DD1h1-1h1-1/D1D1h1-2h1-2/D1D1h1-3h1-3/D1D1h1-4h1-4/D1D1h1-5h1-5/D1D2h2-1h2-1/D2D2h2-2h2-2/D2D2h2-3h2-3/D2D2h2-4h2-4/D2D2h2-5h2-5/D2VI-2: Plot h/D vs. DSee lab manual for detailsh/D = 0.0234D - 0.7225-0.2-0.100.10.20.30.40.50.60.70.0 10.0 20.0 30.0 40.0 50.0 60.0h/DD (cm)h/D vs DVI-3 and VI-4 of the reportVI-3: Using LINEST, determine the slope s, uncertainty in the slope s, the intercept b and the uncertainty in the intercept b. of the plot of h/D vs. D.Using b and bdetermine The equation for determining bin the manual gives the answer in radians. Convert this to degrees. Additionally, using your directly measured values of determine VI-4: Calculate v0twice using s and each value of . Use s, s, b and bto determine v0See lab manual for detailseemmVI-5 and VI-6 of the reportVI-5: Determine the expected value of v0based on the change in height S (not slope s) from the launch position to point A.VI-6: Do VI-4 and VI-5 agree within the uncertainty from VI-4?See lab manual for