Children sled down a 45 m long hill inclined at 26 degrees. At the bottom, the slope levels out. If the coefficient of friction is 0.1, how far do the children slide on the level ground?
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To find how far the children slide on the level ground, we need to first find the distance they slide on the inclined hill, and then use that information to calculate the distance on the level ground.
Step 1: Find the distance on the inclined hill.
Using the given values, we have:
Length of the hill (L) = 45 m and
Angle of inclination (θ) = 26 degrees.
To find the distance on the inclined hill, we can use the formula:
Distance on the inclined hill = L * sin(θ).
Plugging in the values, we get:
Distance on the inclined hill = 45 m * sin(26 degrees).
Step 2: Find the distance on the level ground.
Once the sled reaches the bottom of the hill, it is on the level ground. On the level ground, the only force acting on the sled is the frictional force. The frictional force can be calculated using the formula:
Frictional force = coefficient of friction * Normal force.
Since the sled is on a level ground, the Normal force is equal to the weight of the sled, which can be calculated using the formula:
Weight = mass * gravity.
Step 3: Calculate the distance on the level ground.
To calculate the distance on the level ground, we need to find the frictional force and then use it to calculate the distance using the formula:
Distance on the level ground = force of friction * distance traveled.
Let's calculate each step.
Step 1: Distance on the inclined hill.
Distance on the inclined hill = 45 m * sin(26 degrees).
Step 2: Weight of the sled.
Assuming the mass of the sled is known, we can use the formula:
Weight = mass * gravity.
Step 3: Frictional force on the level ground.
Frictional force = coefficient of friction * Normal force.
Step 4: Distance on the level ground.
Distance on the level ground = frictional force * distance traveled.
By following these steps, you can find the distance the children slide on the level ground.