An object of mass 200 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy force of StartFraction 1 Over 40 EndFraction times the weight of the object is pushing the object up (weight = mg). If we assume that water resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10 N-sec/m, find the equation of motion of the object. After how many seconds will the velocity of the object be 50 m/sec? Assume that the acceleration due to gravity is 9.81 m divided by sec squared .

= 7.08 s

Explanation:

Given that,

- The mass of the object m = 200 kg

- The buoyancy force F_b = W / 40

- The weight of the object = W = m*g

- Water resistance F_w = k*v

- Where, k = 10 Ns/m

Use Newton's Second law of motion to evaluate the acceleration a.

                                    F_net = m*a

                               W - W/40 - 10*v = m*a

                                a = 39/40*g - 10/m *v

                                a = 39/40 * 9.81 - 10/200 * v

                                a = 9.56 - 0.05*v

- Using the first kinematic equation of motion we have:

                                v_f = v_i + a*t

object was dropped from rest, v_i = 0, Hence:

                                v_f = (9.56 -0.05*v)*t  

                               v_f = 9.56*t / ( 1 + 0.05*t)

Find the time t when v_f = 50 m/s

                                50(1 + 0.05*t) = 9.56*t

                                 50 + 2.5*t = 9.56*t

                                 t = 50 / 7.06

                                     = 7.08 s

weather forecasts are done by collecting data about the current state of the atmosphere mainly the temperature, humidity and wind and using meteorology, to determine the atmosphere that evolves over time. the h and l mean the high and low pressure. the red strip is a warm front. the blue strip is a cold front. the blue and red strip is a stationary front. the purple strip is a occluded front.

explanation: