Question

A student is rolling down a slope of 5° with his skateboard. Neglecting the friction in the wheels and assuming he weighs 70 kg, his frontal area is 0.7 m2, and his drag coefficient is 1.1, calculate his terminal velocity (rho = 1.2 kg/m³).

Answer 1

To find the skateboarder’s terminal velocity, balance the gravitational force component along the slope with the drag force, using the drag force formula and solving for velocity.

Step-by-step explanation:

To calculate the terminal velocity of a skateboarder rolling down a slope, we must balance the gravitational force component along the slope with the drag force. The drag force can be calculated using the formula Fd = 1/2 × rho × v^2 × Cd × A, where Fd is the drag force, rho is the air density, v is the velocity, Cd is the drag coefficient, and A is the frontal area.

The gravitational force component along the slope is Fg = m × g × sin(theta), where m is mass, g is acceleration due to gravity, and theta is the slope angle. At terminal velocity, these two forces are equal: Fg = Fd. So, we set m × g × sin(theta) = 1/2 × rho × v^2 × Cd × A and solve for v to find the terminal velocity.

The mass of the skateboarder is 70 kg, the slope angle is 5°, the frontal area is 0.7 m², the drag coefficient is 1.1, and air density is 1.2 kg/m³. Plugging these values into the above equation and solving for v will provide the terminal velocity in meters per second, which can then be converted into kilometers per hour.