Take J to have a magnitude of 60.0 cm and a direction of 270 degrees from the ho

Question

Take J to have a magnitude of 60.0 cm and a direction of 270 degrees from the horizontal. L has a magnitude of 80.0 cm and is directed at some angle, theta, from the horizontal. a.) Compute the magnitude of their sums in terms of theta. B.) what value of theta yields the max magnitude of their sum? What is the max magnitude?c.) What value of theta yields the minimum magnitude of their sum? What is the minimum magnitude? d.) anticipate the answers to (b) and (c) from a conceptual(geometric) vantage without relying on the analytic result from (a).

Explanation / Answer

a] Sum = sqrt(60^2+80^2+2*60*80* cos (theta - 270 degree))

b] For maximum sum, cos (theta - 270 degree) is 1

theta = 270 degree

max sum = sqrt(60^2+80^2+2*60*80) = 140 cm

c]

For maximum sum, cos (theta - 270 degree) is -1

theta = 90 degree

max sum =  sqrt(60^2+80^2-2*60*80) = 20cm

d] For maximum value of sum, L and J should be in same direction and for minimum sum, they should be in opposite.

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