1979M2. A ferryboat of mass M1=2.0×105 kilograms moves toward a docking bumper of mass M2 that is attached to a shock absorber. Shown below is a speed v vs. time t graph of the ferryboat from the time it cuts off its engines to the time it first comes to rest after colliding with the bumper.
At the instant it hits the bumper, t=0 and v=3 meters per second.
a. After colliding inelastically with the bumper, the ferryboat and bumper move together with an initial speed of 2 meters per second. Calculate the mass of the bumper M2.
b. After colliding, the ferryboat and bumper move with a speed given by the expression v=2e−4t. Although the boat never comes precisely to rest, it travels only a finite distance. Calculate that distance.
c. While the ferryboat was being slowed by water resistance before hitting the bumper, its speed was given by 1/v=1/3+βt, where β is a constant. Find an expression for the retarding force of the water on the boat as a function of speed.