A helicopter takes off over level ground, first rising vertically to a height of 146m, then flying a straight-line distance of 268 m at an angle of 32.2 degrees above horizontal.
What is the height of the helicopter at the end of these two displacements (in meters)?
If the sun is shining straight down (so that the shadow of the helicopter is always vertically below the helicopter), then what is the distance between helicopter’s shadow and the takeoff point at the end of the two displacements (in meters)?
Well, it seems like the helicopter was quite ambitious with its vertical and horizontal moves! Let's break it down, shall we?
First, the helicopter rises vertically to a height of 146 meters. So, we know that the initial height of the helicopter is 146 meters.
Next, it flies a straight-line distance of 268 meters at an angle of 32.2 degrees above horizontal. Now, let's imagine these two displacements as the legs of a right-angled triangle, with the height being the vertical displacement and the distance being the horizontal displacement.
To find the height of the helicopter at the end of these two displacements, we need to find the vertical component of the displacement. We can do that by multiplying the distance (268 meters) by the sine of the angle (32.2 degrees).
Vertical component = 268 m * sin(32.2°)
Now, to find the distance between the helicopter's shadow and the takeoff point, we need to find the horizontal component of the displacement. This can be done by multiplying the distance (268 meters) by the cosine of the angle (32.2 degrees).
Horizontal component = 268 m * cos(32.2°)
Finally, using these components, we can find the height of the helicopter at the end by adding the initial height (146 meters) and the vertical component.
Height at the end = 146 m + Vertical component
As for the distance between the helicopter's shadow and the takeoff point, it is simply the horizontal component.
So, using these calculations, you can find the height of the helicopter at the end and the distance between its shadow and the takeoff point. Happy math-ing!
To find the height of the helicopter at the end of the two displacements, we need to find the vertical component of the second displacement and add it to the initial height.
Step 1: Find the vertical component of the second displacement.
Vertical component = distance * sin(angle)
Vertical component = 268m * sin(32.2 degrees)
Vertical component = 268m * 0.5299
Vertical component ≈ 142.27m
Step 2: Add the vertical component to the initial height.
Total height = initial height + vertical component
Total height = 146m + 142.27m
Total height ≈ 288.27m
Therefore, the height of the helicopter at the end of the two displacements is approximately 288.27 meters.
To find the distance between the helicopter's shadow and the takeoff point, we need to find the horizontal component of the second displacement.
Step 3: Find the horizontal component of the second displacement.
Horizontal component = distance * cos(angle)
Horizontal component = 268m * cos(32.2 degrees)
Horizontal component = 268m * 0.8480
Horizontal component ≈ 227.07m
Therefore, the distance between the helicopter's shadow and the takeoff point at the end of the two displacements is approximately 227.07 meters.
To find the height of the helicopter at the end of the two displacements, we need to break down the motion into vertical and horizontal components.
Let's start by finding the vertical component of the helicopter's motion. The helicopter rises vertically to a height of 146 m. This means the vertical displacement is 146 m.
Next, we need to find the horizontal component of the helicopter's motion. The helicopter flies a straight-line distance of 268 m at an angle of 32.2 degrees above the horizontal. To find the horizontal displacement, we can use trigonometry.
The horizontal displacement (d_horizontal) can be calculated using the formula: d_horizontal = d * cos(theta), where d is the total distance and theta is the angle with respect to the horizontal.
Plugging in the values, we have: d_horizontal = 268 * cos(32.2)
Now, to find the height of the helicopter at the end, we need to add the vertical displacement to the original height. Therefore, the height of the helicopter at the end is:
Height = Initial height + Vertical displacement
= 0 + 146
Now, let's move on to calculating the distance between the helicopter's shadow and the takeoff point at the end of the two displacements.
Since the sun is shining straight down, the shadow will always be vertically below the helicopter. Therefore, the horizontal distance between the shadow and the takeoff point will be equal to the horizontal displacement.
Thus, the distance between helicopter's shadow and the takeoff point at the end is:
Distance = Horizontal displacement
= d_horizontal
To summarize:
- The height of the helicopter at the end of the two displacements is 146 meters.
- The distance between the helicopter's shadow and the takeoff point at the end is the horizontal displacement, which can be calculated using the formula d_horizontal = 268 * cos(32.2).