An apple falls from an apple tree growing on a 20° slope. The apple hits the ground with an impact velocity of 5.7 m/s straight downward. What is the component of the apple's impact velocity parallel to the surface of the slope?
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To find the component of the apple's impact velocity parallel to the surface of the slope, we need to use trigonometry and break down the velocity into its vertical and horizontal components.
First, let's find the vertical component of the impact velocity. Since the apple falls straight downward, the vertical component of the velocity is equal to the total velocity. In this case, the vertical component is 5.7 m/s.
Next, we can find the horizontal component of the velocity. Since the apple falls on a slope, the horizontal component of the velocity is affected by the slope angle. To find this component, we need to find the horizontal distance the apple traveled before hitting the ground.
Given that the apple falls from a tree growing on a 20° slope, we can use trigonometry to calculate the horizontal distance. The horizontal distance is equal to the product of the total distance and the cosine of the angle.
Let's assume the total distance traveled by the apple before hitting the ground is D. Then, the horizontal distance is D * cos(20°).
Now, we need to find the time it takes for the apple to fall to the ground. We can use the equation of motion: d = v_0 * t + (1/2) * a * t^2, where d is the total distance, v_0 is the initial velocity (0 m/s in this case since the apple starts from rest), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time.
For the vertical motion, the distance is equal to the vertical component of the velocity multiplied by time, which gives us D = 5.7 * t - (1/2) * 9.8 * t^2.
Now, we can solve this equation to find the time t it takes for the apple to fall.
Once we have the value of t, we can substitute it back into the equation D = 5.7 * t - (1/2) * 9.8 * t^2 to find the total distance D traveled by the apple.
Finally, we can calculate the horizontal component of the impact velocity by multiplying the total distance D by the cosine of the slope angle (cos(20°)). This will give us the component of the impact velocity parallel to the surface of the slope.