1. The problem statement, all variables and given/known data This is a standard projectile motion problem, the mass is m, the drag is F_r = - alpha *v, where alpha is a positive retarding coefficient. The origin is the ground and at time t = 0 the horizontal and vertical velocities are positive a) Write down Newton's second law for the horizontal component of the velocity, v_x (t). Solve for v_x (t) with given initial conditions and use the characteristic time, tau = m/alpha in your answer. Give physical reasoning as to why m increases with tau and why alpha decreases with tau. b) Integrate v_x (t) from a to determine x(t) with given initial conditions. What is x(t) with the limit t goes to infinity? What would be the horizontal position at t = tau? c) Convert the DE from a into an equation for v_x (x). Solve for v_x (x) with the given initial conditions and use tau in your answer. 2. Relevant equations F = ma 3. The attempt at a solution a) F_x = m*v'_x = - alpha*v_x v'_x/v_x = d/dt *ln(v_x) = - alpha * v_x ln v_x = - alpha/m t + ln v_x0 v_x (t) = v_x0 * e^(-t/tau) b) I am stuck here, I integrate to get integral v_x (t) = x(t) = v_x0 *e^(1-t/tau) / (1-t/tau) * A (where A is an arbitrary constant of integration) But solving for A with the condition that x(t=0) = 0 I get A = 0 c) I am stuck here too, m dv_x/dx * dx/dt = - alpha * v(t) I don't know how the convert the second v(t) into a v(x) Any help would be much appreciated.