6. (3 points) An object is released from an airplane that is flying in the horizontal...

Transcribed Image Text:

6. (3 points) An object is released from an airplane that is flying in the horizontal direction with speed VA, as depicted in Figure 10. The force of drag on the object is given by: where b is a positive coefficient, and F = -bv is the velocity of the object. (a) Find expressions for the x and y components of the velocity of the object as a function of time. Hint: You should first show that you can obtain the two following equations: dvx b -Vx dt m b = 9 Vy M dvy dt by applying Newton's Second Law at some point on the trajectory of the object, when the velocity vector of the object makes some angle with the horizontal. Note that the velocity vector is anti-parallel to the drag force, and use that to write out the two components of Newton's Second Law to obtain the equations above. (b) Plot the x and y components of the velocity as a function of time. (c) Show that the terminal velocity of the object is vertical, and determine its magnitude. Page 2 Figure 10: An object dropped from a moving airplane. 6. (3 points) An object is released from an airplane that is flying in the horizontal direction with speed VA, as depicted in Figure 10. The force of drag on the object is given by: where b is a positive coefficient, and F = -bv is the velocity of the object. (a) Find expressions for the x and y components of the velocity of the object as a function of time. Hint: You should first show that you can obtain the two following equations: dvx b -Vx dt m b = 9 Vy M dvy dt by applying Newton's Second Law at some point on the trajectory of the object, when the velocity vector of the object makes some angle with the horizontal. Note that the velocity vector is anti-parallel to the drag force, and use that to write out the two components of Newton's Second Law to obtain the equations above. (b) Plot the x and y components of the velocity as a function of time. (c) Show that the terminal velocity of the object is vertical, and determine its magnitude. Page 2 Figure 10: An object dropped from a moving airplane.