Physics Practice Problems Dynamics with Resistive Forces Practice Problems Solution: A seaplane of total mass m lands on a lake with in...

Solution: A seaplane of total mass m lands on a lake with initial speed v i î. The only horizontal force on it is a resistive force on its pontoons from the water. The resistive force is proportional to the velocity of the seaplane: R = -bv. Newton’s second law applied to the plane is -bvî = m(dv/dt)î. From the fundamental theorem of calculus, this differential equation implies that the speed changes according to the formula below. Carry out the integration to determine the speed of the seaplane as a function of time.

Problem

A seaplane of total mass m lands on a lake with initial speed v . The only horizontal force on it is a resistive force on its pontoons from the water. The resistive force is proportional to the velocity of the seaplane: R = -bv. Newton’s second law applied to the plane is -bv = m(dv/dt). From the fundamental theorem of calculus, this differential equation implies that the speed changes according to the formula below. Carry out the integration to determine the speed of the seaplane as a function of time.