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Give an example of when you’d use a combined plane change vs a simple plane change. (2 examples, one for each type of plane change)

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15. Given a vector field F= 2xi + 3xy) that represents the force of the wind on a sailboat, what is the work done by the wind on a boat traveling along a path defined by y = x² from a position (1,1) to a position (5,25)? Assume positions are given in kilometers and that force is in newtons.
D and E only thank you
An average froghopper insect has a mass of 11.3 mg and jumps to a maximum height of 308 mm when its takeoff angle is 58.0∘ above the horizontal. Find the takeoff speed of the froghopper. Takeoff speed: How much kinetic energy did the froghopper generate for this jump? Express your answer in microjoules. kinetic energy: How much energy per unit of body mass was required for the jump? Express your answer in joules per kilogram of body mass. energy per unit body mass:
A particle moves in the xy plane from the origin to a point having coordinates x=7 m and y=4 m under the influence of a force given by F= -2y^2i -2xj.
Ch.8 Problem #86
REMARKS Only simple geometries-rectangles and triangles-can be solved exactly with this method. More complex shapes require calculus or the square-counting technique in the next worked example. QUESTION When stretching springs, does half the displacement require half as much work? (Select all that apply.) U > Yes, because the work is equal to the force times the distance. Yes, because the spring exerts a constant force. Yes, because half the displacement means the force from the spring is half as large. No, because the spring does not exert a constant force. No, because the force of the spring is proportional to x. No, because the force exerted by the spring is proportional to x². X Consider the expression for the work done by an applied force. Under what conditions is the work done equal to simply a value of the force multiplied by the displacement? Do those conditions apply to the present problem - consider why or why not. Consider how the force exerted by the spring depends on its…
Question: Three identical 5.6 kg spheres are located at 3 of the 4 corners (top left, top right, and bottom right) of a square whose sides are 2.8 m in length. How much work must be done on the gravitational field produced by the spheres in order to remove the top right sphere (place it at infinity)? Assume that the 2 spheres that are left behind (top left, bottom right) remain located on opposite corners of the square. A) 1.50 x 10-9 J B) 5.34 x 10-10 J C) 1.89 x 10-10 J D) 2.67 x 10-10 J E) 5.29 x 10-10 J OA E B. C.
How did you solve D? Wouldn't it's distance be different from that of Point 1 to Point 2 as would be Point 3 to Point 2 and shouldn't that effect the answer for work needed to be done?
Given a vector field F=2xi+3xyj that represents the force of the wind on a sailboat, what is the work done by the wind on a boat traveling along a path defined by y=x^2 from a position (1,1) to a position (5,25)? Assume positions are given in kilometers and that force is in newtons. Note: To make units easy, a newton times a meter is a joule. A newton times a kilometer is a kilojoule (kJ). But F returns newtons.