Skydiver

Calculus Level 1

Two forces act on a parachutist. One is \(mg,\) the attraction by the earth, where \(m\) is the mass of the person plus equipment and \(g=9.8 \text{ m/sec}^2\) is the acceleration of gravity. The other force is the air resistance ("drag"), which is assumed to be proportional to the square of the velocity \(v(t)\).

Using Newton's second law of motion (mass \(\times\) acceleration = net force applied), set up an ordinary differential equation for \(v(t).\)

Let \(k\) denote the drag coefficient.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.