A snow-covered ski slope makes an angle of θslope = 34.0° with the horizontal. When a ski jumper plummets onto the hill, a parcel of splashed snow is thrown up to a maximum displacement of 1.10 m at θsnow = 24.0° from the vertical in the uphill direction as shown in the figure below.
(a) Find the component of its maximum displacement parallel to the surface.
m
(b) Find the component of its maximum displacement perpendicular to the surface.
m
To find the components of the maximum displacement, we need to use trigonometric functions. Let's break down the problem step by step.
(a) To find the component of maximum displacement parallel to the surface, we need to determine the horizontal displacement. We can use the angle θsnow and the maximum displacement distance of 1.10 m.
Using trigonometry, we can determine that the horizontal displacement is given by:
Horizontal displacement = Maximum displacement * cos(θsnow)
Now we can substitute the values:
Horizontal displacement = 1.10 m * cos(24.0°)
Using a calculator, we find:
Horizontal displacement = 1.10 m * 0.9135 ≈ 1.0048 m
Therefore, the component of the maximum displacement parallel to the surface is approximately 1.0048 m.
(b) To find the component of the maximum displacement perpendicular to the surface, we need to determine the vertical displacement. We can use the angle θslope and the maximum displacement distance of 1.10 m.
Using trigonometry, we can determine that the vertical displacement is given by:
Vertical displacement = Maximum displacement * sin(θslope)
Now we can substitute the values:
Vertical displacement = 1.10 m * sin(34.0°)
Using a calculator, we find:
Vertical displacement = 1.10 m * 0.5592 ≈ 0.6151 m
Therefore, the component of the maximum displacement perpendicular to the surface is approximately 0.6151 m.
a) Well, parallel to the surface, huh? Sounds like this snow really wants to go with the flow! To find the component of its maximum displacement parallel to the surface, we need to use some trigonometry. Let's break it down.
We know that the maximum displacement of the snow is 1.10 m. Now we need to find the component parallel to the surface. Since the snow makes an angle of 24.0° from the vertical in the uphill direction, we can use this angle.
Using some trigonometric magic, we can use the sine function to find the parallel component. The formula is:
Parallel component = Maximum displacement * sin(angle)
So, plugging in the values we have:
Parallel component = 1.10 m * sin(24.0°)
And voila! Just punch it in your calculator and you'll find the answer.
b) Now let's talk about the component of the maximum displacement perpendicular to the surface. This snow is really taking its own path, isn't it?
To find this component, we can use the cosine function. The formula is:
Perpendicular component = Maximum displacement * cos(angle)
So, now let's plug in the values:
Perpendicular component = 1.10 m * cos(24.0°)
Calculate that, and you'll get the answer you're looking for.
Hope that helps! Stay snowy!
To find the component of the maximum displacement parallel to the surface (a), we can use trigonometry.
Given:
θslope = 34.0°
θsnow = 24.0°
Maximum displacement = 1.10 m
First, let's find the component of the maximum displacement parallel to the surface.
Step 1: Convert the angles to radians.
θslope = 34.0° × π/180 ≈ 0.593 rad
θsnow = 24.0° × π/180 ≈ 0.418 rad
Step 2: Find the component of the maximum displacement parallel to the slope.
Parallel component = Maximum displacement × cos(θslope - θsnow)
Parallel component = 1.10 m × cos(0.593 - 0.418)
Parallel component ≈ 1.10 m × cos(0.175)
Parallel component ≈ 1.10 m × 0.984
Parallel component ≈ 1.0824 m
Therefore, the component of its maximum displacement parallel to the surface is approximately 1.0824 m.
Now, let's find the component of the maximum displacement perpendicular to the surface (b).
Step 1: Find the component of the maximum displacement perpendicular to the slope.
Perpendicular component = Maximum displacement × sin(θslope - θsnow)
Perpendicular component = 1.10 m × sin(0.593 - 0.418)
Perpendicular component ≈ 1.10 m × sin(0.175)
Perpendicular component ≈ 1.10 m × 0.174
Perpendicular component ≈ 0.1914 m
Therefore, the component of its maximum displacement perpendicular to the surface is approximately 0.1914 m.
So, the answers are:
(a) The component of its maximum displacement parallel to the surface is approximately 1.0824 m.
(b) The component of its maximum displacement perpendicular to the surface is approximately 0.1914 m.