Physics students roll a can of soup from the top of a 3 m long ramp down to the ground. The ramp has an angle of 20° from the ground. Find the x-component and y-component for the displacement vector of the can at the bottom of the ramp with respect to the starting position at the top of the ramp.
X = 3*Cos20.
Y = 3*sin20.
To find the x-component and y-component of the displacement vector of the can at the bottom of the ramp, we can use trigonometry.
First, let's define our coordinate system. We'll take the x-axis to be parallel to the ground and the y-axis to be perpendicular to the ground, pointing upwards.
The x-component of the displacement vector represents the horizontal displacement of the can. Since the ramp is inclined at an angle of 20° from the ground, the x-component can be found using the equation:
x = distance * cos(angle)
In this case, the distance is the length of the ramp, which is 3 m, and the angle is 20°. So we have:
x = 3 m * cos(20°)
Using a calculator, we can evaluate cos(20°) to be approximately 0.9397. Therefore, the x-component is:
x ≈ 3 m * 0.9397 ≈ 2.819 m
Now let's find the y-component of the displacement vector, which represents the vertical displacement of the can. Using the same equation as before, but replacing cosine with sine, we can calculate the y-component:
y = distance * sin(angle)
Plugging in the values:
y = 3 m * sin(20°)
Evaluating sin(20°) to be approximately 0.3420, we find:
y ≈ 3 m * 0.3420 ≈ 1.026 m
Therefore, the x-component of the displacement vector is approximately 2.819 m and the y-component is approximately 1.026 m.