a roller coaster moves 85m horizonally, then travels 45m at an angle of 30 degrees above the horizontal. what is its displacement from its starting point?
85 + 45 cos 30 = 124.0 m horizontally
45 sin 30 = 22.5 m vertically
The magnitude of the displacement is
(124^2 + 22.5^2)
A roller coaster. Move 85m horizontally then
Well, it sounds like this roller coaster is really going the extra mile, or should I say meters! Let's break it down.
First, it moves 85m horizontally, which means there is no vertical displacement. So, we can rule out any height change.
Then, it travels 45m at an angle of 30 degrees above the horizontal. This means it moved both vertically and horizontally. To find the vertical displacement, we can use some trigonometry. The vertical component is given by 45m multiplied by the sine of 30 degrees, which is (45m) * sin(30 degrees) = 22.5m.
Now, let's find the horizontal displacement. It's still 45m, but this time we use the cosine of 30 degrees, which is (45m) * cos(30 degrees) = 38.94m.
Finally, we can calculate the overall displacement by finding the vector sum of the horizontal and vertical displacements. So, using the Pythagorean theorem, we have displacement = √(38.94m² + 22.5m²). This gives us an approximate displacement of 45.1 meters.
So, the roller coaster has a displacement of approximately 45.1 meters from its starting point. Now that's a wild ride!
To find the displacement of the roller coaster from its starting point, we need to calculate the horizontal and vertical components of the displacement separately.
First, let's find the horizontal component of the displacement. The roller coaster moves 85m horizontally, which means its horizontal displacement is also 85m.
Next, let's find the vertical component of the displacement. The roller coaster travels 45m at an angle of 30 degrees above the horizontal. To find the vertical displacement, we can use trigonometry. The vertical displacement can be calculated as follows:
Vertical displacement = 45m * sin(30 degrees)
Using a calculator, sin(30 degrees) is equal to 0.5. Therefore, the vertical displacement is:
Vertical displacement = 45m * 0.5 = 22.5m
Now, using the horizontal and vertical components of displacement, we can calculate the resultant displacement using the Pythagorean theorem. The resultant displacement is the hypotenuse of a right-angled triangle, with the horizontal and vertical components as the other two sides.
Resultant displacement = sqrt((Horizontal displacement)^2 + (Vertical displacement)^2)
Resultant displacement = sqrt((85m)^2 + (22.5m)^2)
Resultant displacement = sqrt(7225m^2 + 506.25m^2)
Resultant displacement = sqrt(7725.25m^2)
Resultant displacement ≈ 87.87m
Therefore, the displacement from its starting point is approximately 87.87 meters.
85 + 45 cos 30 = 124.0 m horizontally
45 sin 30 = 22.5 m vertically
The magnitude of the displacement is
sqrt(124^2 + 22.5^2)