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| Math Central | Quandaries & Queries |
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Question from kwame, a student: the range R of projectile fired with an initial velocity Vo ,at an angle of elevation (@ )theta from the horizontal is given by the equation R = (Vo(squared) sin(2theta)/g. where g is the acceleration due to gravity . Find the angle theta such that the projectile has maximum range . |
Kwame,
Vo and g are constants and hence R is a function of θ alone.
R(θ) = Vo2 sin(2θ)/g
Since Vo and g are constants you can differentiate R(θ) with respect to θ to get
R'(θ) = 2 Vo2 cos(2θ)/g
Solve R'(θ) = 0 for θ and then use the second derivative to verify that this value of θ yields a maximum value.
Harley
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