projectile motion project
DESCRIPTION
A project I put together to help students master Algebra I, Algebra II, or Pre-Calculus using technology and writing code in order to aid them in conceptualizing mathematical ideas.TRANSCRIPT
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In[30]:= H*Reset variables*LClear@H, RD
Do@Print@D, 89
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In[30]:=
theta = ArcTan@H4 H RLD;
H*Magnitude of the initial velocity*Lv0 = Sqrt@H2 * g * H HR^2 + 16 * H^2LL H16 * H^2LD;
vy = v0 * Sin@thetaD;vx = v0 * Cos@thetaD;
H*Determinig time t1 and t2 at which the ball is 10 ft from the ground*Lsolt = Simplify@Solve@-16 t^2 + vy * t - 10 0, tDD;t1 = t . solt@@1DD;t2 = t . solt@@2DD;
H*Using time t1 and t2 to determine thehorizontal distance travelled in those times*L
xt1 = vx * t . solt@@1DD;xt2 = vx * t . solt@@2DD;
Print@"The ball is kicked at an angle of ", H180 * theta PiL," degrees, and with an initial velocity magnitude of ", v0,
" feet per second. It follows that the kinematic equations HtL= xHtL+ yHtL =Hv_x*tL + H.5*g*t^2 + v_y*tL for the scenario matchingthese condions are HtL= H", vx, "tL + H", .5 * g, "t^2 + ", vy, "tL "D
Print@"Using the equations of motion the ball is first ten feetfrom the ground during its ascend after it has travelled for ",
t1, " seconds, and it has travelled ", xt1,
" feet along the horizontal, and again during its descend after
it has travelled ", t2, " seconds, and it has travelled ", xt2,
" feet along the horizontal. It follows that the player must stand at the ",
HHxt2 - 30L 3L, " yard line to be at the maximum distance fromthe field goal post and still clear the field goal. Furthermore
the path using the equations of motion looks as follows: "D
H*Plot of the equations of motion*LParametricPlot@8vx * u, -.5 * g * u^2 + vy * u
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HeightMax = 90
RangeMax = 127.5
A = -0.0221453
B = 2.82353
The Quadratic equation satisfying these conditions is y = -0.0221453x2+ 2.82353x
The ball is first ten feet from the ground during its ascend after it has travelled
3.64592 feet horizontally, and again during its descend after it has travelled
123.854 feet horizontally. It follows that the player must stand at the
31.2847 yard line to be at the maximum distance from the field goal post
and still clear the field goal. Furthermore the path looks as follows:
Out[41]=
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The ball is kicked at an angle of 70.4976
degrees, and with an initial velocity magnitude of 80.514
feet per second. It follows that the kinematic equations HtL= xHtL + yHtL=Hv_x*tL + H.5*g*t^2 + v_y*tL for the scenario matching these condions are HtL= H
26.8794tL + H16.t^2 + 75.8947tLUsing the equations of motion the ball is first ten feet from the ground during its
ascend after it has travelled for 0.13564 seconds, and it has travelled
3.64592 feet along the horizontal, and again during its descend after it has travelled
4.60778 seconds, and it has travelled 123.854
feet along the horizontal. It follows that the player must stand at the 31.2847
yard line to be at the maximum distance from the field goal post and still clear the
field goal. Furthermore the path using the equations of motion looks as follows:
Projectile motion main.nb 3
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Out[58]=
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4 Projectile motion main.nb