By Barus C.

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1–13 the vectors are arranged as the sides of a parallelogram with F sin θ the height of the parallelogram. The product rF sin θ is the magnitude of r × F and is also the area of the parallelogram (a base times the height) formed by r and F. The second definition of the cross product is mathematically easier but harder to relate to physical problems. This definition is expressed as a determinant. 1–8 Form the cross product of A = 23<37° and C = 47 <193°. Solution: The vectors and their components are shown in Fig.

What (boat) speed is necessary to have the package land in the boat? 7s = 14m/s <><><><><><><><><><><><> 3–9 You are observing steel balls falling at a constant velocity in a liquid-filled tank. The window you are using is one meter high and the bottom of the window is twelve meters from the bottom of the tank. 0s to pass the window. Calculate the time required to reach the bottom of the tank, after the ball has reached the bottom of the window. Solution: The situation is diagrammed in Fig. 3–7.

Getting a sign wrong is the source of many, possibly most, errors in falling body problems. Fig. 0t -40 = 0, with solution The positive time is the obvious choice. Note the numbers used for the solutions to the quadratics in time for this and problem 3-2. The velocity when the ball strikes the ground is Notice that whether the v term is a positive or negative number, the result is the same. If the ball is thrown up with a certain velocity or down with the same velocity, the velocity at impact is the same.