1. The problem statement, all variables and given/known data A projectile of mass m is projected vertically upwards with speed U. In addition to its weight it experiences a resistive force mkv^2, where v is the speed at which the projectile is moving and k is a constant. Derive the equation of motion of the projectile: dv/dt = -(g + kv^2) Derive a differential equation for v as a function of z, where z is the height of the projectile above its starting position. Solve this equation to find the maximum height reached by the projectile. 3. The attempt at a solution F = ma = m dv/dt -mg - mkv^2 = m dv/dt dv/dt = -g - kv^2 = -(g + kv^2) dv/dt = dv/dz * dz/dt = v dz/dt v dv/dz = -(g + kv^2) [v/(g+kv^2)] dv = - dz Integrating: 1/2k ln(g + kv^2) = -z + C ln(g + kv^2) = -2kz + 2kC When v = U, z = 0, 2kC = ln(g + kU^2) ln(g + kv^2) = -2kz + ln(g + kU^2) 2kz = ln([g+kU^2]/[g+kv^2]) Maximum z is when v = 0. z = 1/2k ln((g + kU^2)/(g)) = 1/2k ln(1 + kU^2/g) Is this correct? Thankyou.