An object moving in a liquid experiences a linear drag force: d= (bv, direction opposite the motion), where b is constant called the drag coefficient. for a sphere of radius r, the drag constant can be computed as b = 6πηr, where η is the viscosity of the liquid. a. use what you've learned in calculus to prove thatb. find an algebraic expression for , the x-component of velocity as a funtion of distance traveled, for a spherical particle of radius r and mass m that is shot horizontally with initial speed through a liquid viscosity η.c. water at 20°c has viscosity . suppose a 1.0-cm-diameter, 1.0 g marble is shot horizontally into a tank of 20°c water at 10 cm/s. how far will it travel before stopping?

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.