Question

You are on a sled at the top of a hemispherical, snowy hill of radius 17 m. you begin to slide down the hill. how fast are you moving in m/s when you have made it 25 degrees down the hemisphere as seen below? ignore friction.

Answer 1

To determine the speed at which you are moving 25 degrees down the hemisphere, we can use the principles of circular motion and conservation of energy equation. Using a radius of 17 m and an angle of 25 degrees, we can calculate the vertical distance traveled. Plugging in the values, the speed is approximately 7.99 m/s.

Step-by-step explanation:

To determine the speed at which you are moving when you have made it 25 degrees down the hemisphere, we can use the principles of circular motion and conservation of energy. The initial potential energy at the top of the hill is converted into kinetic energy as you slide down. We can calculate the speed using the conservation of energy equation:

Initial potential energy = Final kinetic energy

mgh = 1/2 mv^2

Where m is the mass, g is the acceleration due to gravity, h is the height, and v is the speed of the sled. In this case, the height is the vertical distance traveled while going 25 degrees down the hemisphere, which is r(1-cos(25)).

Plugging in the values and solving for v:

v = sqrt(2gh) where g is the acceleration due to gravity (9.8 m/s^2) and h is the vertical distance.

Using a radius of 17 m and an angle of 25 degrees, we can calculate the distance:

h = 17(1-cos(25)) ≈ 2.49 m

Plugging in the values:

v = sqrt(2 * 9.8 * 2.49) ≈ 7.99 m/s

Therefore, when you have made it 25 degrees down the hemisphere, you are moving at a speed of approximately 7.99 m/s.