Materials: Computer and School Network 
Time Allotment: 4 Class Days 
This activity simulates an archery contest in which you are challenged to pop a target balloon from a great distance. In the process you will learn about projectile motion. You will investigate the advantages of looking at a problem from more than one perspective. In particular, you will approach this task using two different coordinate systems: polar coordinates (Task 1) and Cartesian coordinates (Task 2).
You have a custombuilt crossbow for this competition. It uses a plumb bob to read the launch angle. You have also tested the relationship between the bow extension and the launch velocity of the arrows. Using this information, you've constructed, calibrated and attached a meter to the cranking mechanism. The meter indicates the launch velocity which will be achieved for any given bow extension.
You need to find the correct angle(s) to the horizontal at which the bow must be set in order to hit the target. The launch velocity is fixed at 60 m/s.
Verify this position using an approximated reading off the "Target Screen" grid.
A representative of Renaisance Industries, Inc. comes by with a new crossbow based on a longlost design by Leonardo DaVinci. It uses two bows at right angles to each other, allowing you to separately control the vertical and horizontal velocity components of the arrow. The arrow is on a pivot and it is automatically aimed depending upon the extension of the two bows. For instance, if the vertical bow is not etended at all (v_{y} = 0 m/s), the force from the horizontal bow turns the arrow track completely to the horizontal. If both bows are extended equal amounts, then the arrow is directed at a 45degree angle to the horizontal.
In Task 1, we were concerned with the polar coordinate description of the arrow's velocity  i.e., the speed and angle. Now the Renaisance representative convinces you that using this bizarre contraption will enable you to accurately predict the path of the arrow more easily using cartesian corrdinates  i.e., xvelocity and yvelocity. We have discussed earlier in our course that perpendicular components of motion are independent of each other. The xcomponents of motion have no effect upon the ycomponents of motion, and vice versa. In this task, you will utilize cartesian coordinate system and the principle of the independence of x and ycomponents to ultimately strike the target.
The controls in the Task 2 window allow you to input the x and ycomponents of the velocity independently. (A button and two output boxes provide you with the calculated angle and arrow speed based on these components.)
g*t_{up} + v_{iy} = 0
where g = 9.8 m/s/s (the
acceleration of gravity)
The total time of flight (up and down) is twice the time to travel up.
Initial yvelocity (v_{iy}) = _____________ m/s
Calculated total time of flight:
____________ Show your work
below.
Fire the arrow to check your
prediction.
Initial v_{iy} (m/s) 
Calculated time of flight (s) 
Initial v_{x} (m/s) 
Calculations/Work: 
_________ 
___________ 
_________ 
____________________ 
_________ 
___________ 
________ 
____________________ 
_________ 
___________ 
_________ 
____________________ 
_________ 
___________ 
_________ 
____________________ 
y = 0.5*g*t^2 + v^{y}*t
or in standard quadratic form:
0.5*g*t^2 + v^{y}*t  y =0
Determine the two time of flight values to hit the elevated target and the corresponding v_{x} values. Check your answers by running the simulation with the calculated v_{x} values. Record the data below and your selected v_{x} values for hitting the target. Show the calculations which you used to determine the two v_{x} values required to hit the target.
Hitting Target on Way Up 
Hitting Target on Way Down 
Initial yVelocity = ________ m/s 
Initial yVelocity = ________ m/s 
Measured ydistance = _______ m 
Measured ydistance = _______ m 
Measured xdistance = _______ m 
Measured xdistance = _______ m 
Time of Flight = _______ s 
Time of Flight = _______ s 
Calc'd xvelocity = _________ m/s 
Calc'd xvelocity = _________ m/s 
Work for Calculating xvelocity:

Work for Calculating xvelocity:

Note: you need to remove the "lab walls." Scroll down the Control Panel window to access the "Lab has no walls" control. Click in this control to "remove the walls."
Solve the following problems using the principles which you learned in this lab.
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This page created by Tom Henderson and last updated on 8/7/97.