Marcus and Santa are sliding down a snowy hill that is 13.3 m high. On the hill itself friction and air resistance can be ignored. At the bottom of hill the sled hits a long patch of rough snow that slows the sled down by exerting an average force of 170 newtons. Santa marcus and the sled together are 80 kg. How fast Is the sled traveling after sliding for ten meters on the rough snow?
mgh=170*10+1/2 m v^2
solve for v.
To find the speed of the sled after sliding for ten meters on the rough snow, we can use the principle of conservation of energy.
The initial potential energy of Marcus, Santa, and the sled can be calculated using the formula:
Potential Energy = mass * gravity * height
where mass is the total mass of Marcus, Santa, and the sled (80 kg), gravity is the acceleration due to gravity (9.8 m/s²), and the height is the height of the snowy hill (13.3 m).
Potential Energy = 80 kg * 9.8 m/s² * 13.3 m
Next, we calculate the work done by the rough snow. Since work is equal to force multiplied by distance, we can use the formula:
Work = force * distance
where force is the average force exerted by the rough snow (170 N) and distance is the distance over which the force acts (10 m).
Work = 170 N * 10 m
The work done by the rough snow should be equal to the change in the sled's kinetic energy. Therefore, we can equate the initial potential energy to the final kinetic energy:
Potential Energy = Kinetic Energy
Kinetic Energy = 0.5 * mass * velocity²
where mass is the total mass of Marcus, Santa, and the sled (80 kg), and velocity is the final velocity of the sled.
Since we want to find the final velocity, we need to rearrange the formula:
velocity = √((2 * Potential Energy) / mass)
Substituting the values we have:
velocity = √((2 * (80 kg * 9.8 m/s² * 13.3 m)) / 80 kg)
Now, let's solve the equation step by step to find the final velocity of the sled:
velocity = √((2 * (80 kg * 9.8 m/s² * 13.3 m)) / 80 kg)
velocity = √((2 * (10592 kg·m²/s²)) / 80 kg)
velocity = √(21184 kg·m²/s² / 80 kg)
velocity = √(264.8 m²/s²)
velocity ≈ 16.3 m/s
Therefore, the sled is traveling at approximately 16.3 m/s after sliding for ten meters on the rough snow.