George is pulling Cameron on a toboggan and is exerting a force of 40 N acting at an angle of 60- to the ground- If Cameron is pulled by a distance of 100 m horizontally- then the work done by George is - J

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Standard IX

Mathematics

Dot Product of Two Vectors

George is pul...

Question

George is pulling Cameron on a toboggan and is exerting a force of 40N acting at an angle of $60^{\circ}$ to the ground. If Cameron is pulled by a distance of 100 m horizontally, then the work done by George is __ J

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Solution

See carefully. George is applying 40N at an angle of $60^{\circ}$ to the horizontal direction. This horizontal direction is the same direction in which we are measuring our displacement. So the angle between force and displacement is $60^{\circ}$

$S o w o r k d o n e = \to F . \to d = ∣ ∣ \to F ∣ ∣ ∣ ∣ \to d ∣ ∣ c o s θ = 40 \times 100 \times c o s 60 J = 4000 \times (\frac{1}{2}) J = 2000 J$

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George is pulling Cameron on a toboggan and is exerting a force of 40N acting at an angle of 60∘ to the ground. If Cameron is pulled by a distance of 100 m horizontally, then the work done by George is __ J

George is pulling Cameron on a toboggan and is exerting a force of 40N acting at an angle of $60^{\circ}$ to the ground. If Cameron is pulled by a distance of 100 m horizontally, then the work done by George is __ J