A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º above the horizontal. What is th
e skier's displacement from his starting point? (Use the graphical method to answer and include your scale on the graph paper.) Give both the magnitude and the angle in your answer.
1 answer:
Because there isnt 90 degrees angle in this triangle (triangle - starting point - point where he starts climbing- ending point) we will use cosine law to find magnitude of displacement. For cosine law we need 2 sides of triangle and angle between them which is exactly what is given.
a^2 = b^2 + c^2 - 2*b*c*cos(alpha)
after expressing values we get:
a^2 = 10000 + 1225 + 5734
a = 130,2 meters
to calculate angle we again use cosine law but now our unknown variable is angle alpha. our sides we will use are 100 meters and 130,2 meters because we need angle between them.
cos(alpha) = (b^2 + c^2 - a^2)/(2*b*c)
cos(alpha) = 0.98
alpha = 8.89 degrees
a^2 = b^2 + c^2 - 2*b*c*cos(alpha)
after expressing values we get:
a^2 = 10000 + 1225 + 5734
a = 130,2 meters
to calculate angle we again use cosine law but now our unknown variable is angle alpha. our sides we will use are 100 meters and 130,2 meters because we need angle between them.
cos(alpha) = (b^2 + c^2 - a^2)/(2*b*c)
cos(alpha) = 0.98
alpha = 8.89 degrees
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