A high-speed railway car goes around a flat, horizontal circle of radius 480 m at a constant speed. The magnitudes of the horizontal and vertical components of the force of the car on a 65.0 kg passenger are 208 N and 637 N, respectively. (a) What is the magnitude of the net force (of all the forces) on the passenger? (b) What is the speed of the car?

Net force ( F ) = 208 N.

Speed of car ( v ) = 68.58 m/s.

Explanation:-

The radius ( r ) = 480 m.

Mass of passenger ( m ) = 65 kg.

Horizontal force ( ) = 208 N.

Vertical force ( ) = 637 N.

Net vertical component of force ( ) = m*g - 637   = 65 * 9.8 - 637 =  0 N.

a ) magnitude of net force .

  = 208 N.

b) The speed of car.

   where v is the velocity.

v² = 4704

v = 68.58 m/s.

heat the gas and measure the pressure

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .