1. (16 points) A basketball player runs a pattern shown in the drawing by the th

Question

1. (16 points) A basketball player runs a pattern shown in the drawing by the three vectors A, B and C. The magnitudes of these vectors are A-7.0m, B : 16.0m, c-5.0m. The x-axis lies along a line joining the 2 baskets and the y-axis is perpendicular to the length of the court. 30° 45° Complete the table below by calculating the magnitude and direction of all vector components Hence find the magnitude and direction of the resultant vector A B+C. Use the usual convention for vector directions discussed in class -right" and "up are taken as positive directions. All angles should be written as an angle measured from the positive x-axis. X-COMPONENT Y-COMPONENT MAGNITUDE DIRECTION MacBook Air 20 a 8

Explanation / Answer

For A

Magnitude = 7 m

Direction = 90° Clockwise

x component = 0

y component = -7

Vector form (A) = -7j

For B

Magnitude = 16 m

Direction = 45° Counterclockwise

x component = 16cos(45) = 11.314

y component = 16sin(45) = 11.314

Vector form (B) = 11.314 i + 11.314 j

For C

Magnitude = 5 m

Direction = 30° Clockwise

x component = 5cos(30) = 4.33

y component = -5sin(30) = -2.5

Vector form (C) = 4.33 i - 2.5 j

Resultant Vector (R) = A + B + C

= -7j + 11.314i + 11.314j + 4.33i - 2.5j

= 15.644i + 1.814j

So magnitude of resultant vector = 15.7488

Direction = 6.614° Counterclockwise

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