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If You Throw a Stone into the Air at an Angle

Question 68

Essay

If you throw a stone into the air at an angle of θ\theta to the horizontal, it moves along the curve y=xtanθx2160(1+tan2θ)y=x \tan \theta-\frac{x^{2}}{160}\left(1+\tan ^{2} \theta\right) ,
where y is the height of the stone above the ground, x is the horizontal distance.Suppose the stone is to be thrown over a wall at a fixed horizontal distance l away from you.If you can vary θ\theta , what is the highest wall that the stone can go over? (Your answer will contain l.)

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