ehild said:Have you studied differential equations? That is a first order-separable one.
ehild
The velocity equation for a vertically thrown object with quadratic drag is given by:
v(t) = (mg/c) * (1 - e^(-ct/m)) - (mgt/c)
where v(t) is the velocity at time t, m is the mass of the object, g is the acceleration due to gravity, c is the drag coefficient, and e is the base of the natural logarithm.
The quadratic drag is a type of drag force that is proportional to the square of the velocity, while linear drag is proportional to the velocity. This means that as an object's velocity increases, the quadratic drag force will increase at a faster rate than the linear drag force.
The constant e in the velocity equation represents the base of the natural logarithm. It is a mathematical constant that is approximately equal to 2.71828. It is used to model the decay of the velocity of a vertically thrown object due to quadratic drag.
The mass of the object directly affects the velocity equation by determining the magnitude of the drag force. A heavier object will experience a larger drag force and therefore have a lower velocity compared to a lighter object with the same initial conditions.
No, the velocity equation for quadratic drag is specifically designed for vertically thrown objects. The drag force and acceleration due to gravity act in opposite directions for vertically thrown objects, while they act in the same direction for horizontally thrown objects. Therefore, a different equation is needed to accurately model the velocity of horizontally thrown objects with quadratic drag.