A roller coaster moves 200 ft horizontally, then rises 135 ft at an angle of 30.0° above the horizontal. ?
A roller coaster moves 200 feet horizontally and then rises 135 feet at an angle of 30.0° above the horizontal. Next, it travels 135 feet at an angle of 40.0° below the horizontal. Using graphical techniques, determine the roller coaster’s displacement from its starting point at the end of this movement.
1 Answers
Feb 11, 2025
Draw a picture: http://i279.photobucket.com/albums/kk154/mwettergr…
x_tot = 200 + [135cos(30°)] + [135cos(-40°)]
x_tot = 420.3294293 ft
y_tot = [135sin(30°)] + [135sin(-40°)]
y_tot = -19.27632731 ft
Displacement = √(x² + y²)
Displacement = √[(420.3294293)² + (-19.27632731)²]
Displacement = 420.771204 ft
Displacement = 421 ft
tanθ = (y / x)
tanθ = (-19.27632731 / 420.3294293)
θ = arctan (-0.0458600468)
θ = -2.625747386°
θ = -2.63°
Displacement = 421 ft at 2.63° below the horizontal.
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