Sapling Learning A pinball bounced around its machine before resting between two

Question

Sapling Learning A pinball bounced around its machine before resting between two bumpers. Before the ball came to rest, its displacement (all angles measured counterclockwise from the horizontal x axis) was recorded by a series of vectors. 83 cm at 90 53 cm at 159 69 cm at 227 45 cm at 285 65 cm at 25 Use the figure on the right to draw these displacements in order with the first vector starting at the large X" and then determine the total displacement's magnitude and direction. Number magnitude ? ! cm Note: the vector drawing board above sho be used to answer the question, but your drawing will not be graded Number direction HD

Explanation / Answer

You're supposed to measure the distance from X to the end of vector 5 using the appropriate scale, and measure the angle (counterclockwise from X) using a protractor.

Mathematically:
x = [83cos90+53cos159+69cos227+45cos285+65cos25] cm = -25.98 cm
y = [83sin90+53sin159+69sin227+45sin285+65sin25] cm = 35.53 cm

so d = ?(x² + y²) = 44 cm
and ? = arctan(35.53/-25.98) = -53.8º +180º (to get into QII) = 126.2º

Of course, anything close by ruler and protractor would be fine.

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