A skier coasts down a very smooth 10-m high slope. if the speed of the skier on the slope is 5.0-m/s what is his speed at the bottom of the slope?
That depends upon whether or not the 5.0 m/s speed is the speed at the TOP of the slope. If so, add 2gh = 196 m^2/s^2 to the initial V^2 to calcualte the final V^2.
To find the speed of the skier at the bottom of the slope, we can use the principle of conservation of mechanical energy. Assuming there is no friction, the total energy at the top of the slope is equal to the total energy at the bottom of the slope.
The potential energy of the skier at the top of the slope can be calculated using the formula:
Potential Energy = mass * gravitational acceleration * height
In this case, the height is 10 m.
The kinetic energy of the skier is given by the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Given that the velocity of the skier on the slope is 5.0 m/s, we can plug in the values to calculate the initial potential energy and the initial kinetic energy.
Now, since there is no friction, all the initial potential energy is converted into kinetic energy at the bottom of the slope. Therefore, the final kinetic energy at the bottom of the slope will be equal to the initial potential energy at the top of the slope.
Setting the initial potential energy equal to the final kinetic energy gives us:
mass * gravitational acceleration * height = (1/2) * mass * velocity^2
We can cancel out the mass from both sides of the equation:
gravitational acceleration * height = (1/2) * velocity^2
Now, we can rearrange the equation to solve for velocity:
velocity = sqrt(2 * gravitational acceleration * height)
We know the values of gravitational acceleration (9.8 m/s^2) and height (10 m), so we can plug these values into the equation to calculate the skier's speed at the bottom of the slope.