A roller-coaster car moves 194 ft horizontally and then rises 115 ft at an angle

Question

A roller-coaster car moves 194 ft horizontally and then rises 115 ft at an angle of 32.0 degree above the horizontal. It next travels 115 ft at an angle of 46.0 degree downward (below the horizontal). What is its displacement from its starting point? (Assuming the initial horizontal motion of the car to be along the +x axis.) magnitude ft direction degree counterclockwise from the +x-axis A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are d_1 = 4.04 m to the north, d_2 = 2.04 m northeast, and d_3 = 1.12 m at 30.0 degree west of south (see the figure below), Starting at the same initial point, an expert golfer could make the hole in what single displacement? magnitude m direction

Explanation / Answer

here,

total horizontal distance travelled , x = 194 + 115 * cos(32) + 115 * cos(46)

x = 371.41 ft

total vertical distance , y = 115 * sin(32) - 115 * sin(46)

y = - 21.78 ft

the net diplacement , d = sqrt(x^2 + y^2)

d = 372.04 ft

theta = arctan(y/x)

theta = 3.35 degree

the displacement is 372.04 ft downwards at 3.35 degree

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