For small, slowly falling objects, the assumption made in the text that the drag force is proportional to the velocity is a good one. For larger, more rapidly falling objects, it is more accurate to assume that the drag force is proportional to the square of the velocity.2 a.Write a differential equation for the velocity of a falling object of mass m if the magnitude of the drag force is proportional to the square of the velocity and its direction is opposite to that of the velocity. b.Determine the limiting velocity after a long time. c.If m = 10 kg, find the drag coefficient so that the limiting velocity is 49 m/s. d.Using the data in part c, draw a direction field and compare it with Figure 1.1.3.

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A:

Q: The displacement (in meters) of a particle moving in a straight line is given by the equation of…

A:

Q: The average energy E (in kcal) needed for a lizard to walk or run a distance of 1 km has been…

A: Consider the given average energy.

Q: The fraction of the senior class S, who has heard about the Cross Country Team state victory…

A:

Q: Using Newtons laws of motion we saw that while ignoring air resistance a body falling through the…

A: When air resistance is taken into account, the force due to air resistance is often modeled as being…

Q: The displacement (in meters) of a particle moving in a straight line is given by the equation of…

A: Given: The displacement (in meters) of a particle moving in a straight line is given by the equation…

Q: The rate at which a ceratin disease spreads is proportional to the product of the percentage of the…

A: We have to find the rate R(t) at which disease spreads Constant of  Proportionality = 0.03 Percent…

Q: The equation of motion of a particle is s = t-5t, where s is in meters and t is in seconds. Assuming…

A: Please see the below picture for detailed solution.

Q: A skydiver weighing 120kg drops vertically from a jet flying at 4.000m. Assume the force due to air…

A: Let anet, v be instantaneous acceleration and velocity, respectively.  Net force, Fnet=120 kg·anet…

Q: 15. A remote-controlled train begins moving at t = 0 seconds. Its velocity (in ft/sec) is given by…

A:

Q: The windchill index announced during the winter by the weather bureau measures how cold it "feels"…

A:

Q: Sandy's main house is a hemispherical glass dome with diameter of 8m. Suppose that the glass is m…

A: NOTE: Refresh your page if you can't see any equations. . the diameter of the hemisphere is 8 m so…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.