Comments on: How do you answer this projectile motion problem using vectors? http://dphcustompins.net/how-do-you-answer-this-projectile-motion-problem-using-vectors Just another WordPress weblog Mon, 06 Sep 2010 01:09:49 +0000 hourly 1 http://wordpress.org/?v=3.0.1 By: getfreducated http://dphcustompins.net/how-do-you-answer-this-projectile-motion-problem-using-vectors/comment-page-1#comment-933 getfreducated Wed, 10 Feb 2010 09:14:56 +0000 http://dphcustompins.net/how-do-you-answer-this-projectile-motion-problem-using-vectors#comment-933 The velocity vector (at t=0) is given by V0cosθ i + V0sinθ j (where i and j are unit vectors parallel to the x and y coordinate axes). The vector changes in time... V(t) = Vcosθ i + (Vsinθ -gt) j The position vecor is the integral of the velocity vector, so s(t) = Vcosθ t + (Vsinθ t -1/2 gt^2) j Plugging in our data... s(t) = 40 √2 t i + (40 √2 t - 16 t^2) j When the x value of this vector is 100, t=1.77 s which gives a y position of 150 feet > 48 thus the ball clears the tree. When the y position is 0, t = 3.53 sec and the x position at that time is 200 feet (a respectable shot but not a hole out). =============================================== Reality check... Range = V^2 cos (90) /g = 200 m. so the second part checks using the "non-vector" approach. -Fred That is the method, please check the algebra and aritmatic before submitting. The velocity vector (at t=0) is given by V0cosθ i + V0sinθ j (where i and j are unit vectors parallel to the x and y coordinate axes). The vector changes in time…

V(t) = Vcosθ i + (Vsinθ -gt) j The position vecor is the integral of the velocity vector, so

s(t) = Vcosθ t + (Vsinθ t -1/2 gt^2) j Plugging in our data…

s(t) = 40 √2 t i + (40 √2 t – 16 t^2) j

When the x value of this vector is 100, t=1.77 s which gives a y position of 150 feet > 48 thus the ball clears the tree.

When the y position is 0, t = 3.53 sec and the x position at that time is 200 feet (a respectable shot but not a hole out).
===============================================
Reality check…

Range = V^2 cos (90) /g = 200 m. so the second part checks using the "non-vector" approach.

-Fred

That is the method, please check the algebra and aritmatic before submitting.

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