A roller coaster travels 10.6 m at an angle of 15.0◦ above the horizontal. How far does it move vertically
? Answer in units of m.
IS it 10.6sin15=2.7435m
yes, correct.
To determine the vertical distance traveled by the roller coaster, we need to find the vertical component of the 10.6 m distance traveled at an angle of 15.0 degrees above the horizontal.
The vertical distance can be obtained using the trigonometric function sine (sinθ). The formula for finding the vertical component is as follows:
Vertical distance = Horizontal distance × sin(angle)
In this case, the horizontal distance is 10.6 m and the angle is 15.0 degrees.
Using the formula, we can calculate the vertical distance as follows:
Vertical distance = 10.6 m × sin(15.0°)
To find the sine of 15.0 degrees, you can either use a scientific calculator or look it up on a trigonometric table. The sine of 15.0 degrees is approximately 0.2588.
Now, let's substitute the values back into the equation:
Vertical distance = 10.6 m × 0.2588
Vertical distance ≈ 2.74 m
Therefore, the roller coaster moves vertically approximately 2.74 meters.