Question

1. An airplane leaves airport A and travels in a straight line in a direction 30 degrees East of North at a constant speed of 300km/hr for 40 minutes, then it abruptly changes its direction to 25 degrees South of East and now travels at a constant velocity of 200km/hr for 30 minutes, and finally it abruptly heads directly South and travels at a velocity of 300km/hr for 60 minutes before landing at airport B. (a) calculate the distance, D, and direction that airplane would have to fly to return in a straight line from airport B to airport A. (b) Calculate the magnitude and direction of the average velocity (Vavg) of the airplane in its trip from airport A to airport B. (c) Calculate the average speed of the airplane in its trip from airport A to airport B.

2. At t = 0, a red toy car is set rolling on a straight track with initial position 10.0 cm, initial velocity -4.50 cm/s, and constant acceleration 3.60 cm/s2 . At the same moment, a blue car is set rolling on an adjacent track with initial position 5.00 cm, an initial velocity of +5.50 cm/s, and constant acceleration zero. (a) plot the velocity for each car from t = 0 s to t= 6.0 s (on the same v vs t plot). Label the velocities at time t=0 s and t=6 s. (b) plot the position for each car from t = 0 s to t = 6.0 s (on the same x vs t plot). Label the positions at time t=0 s and t=6 s. (c) At what time, if any, do the two cars have equal speeds (calculate exactly if possible)? (d) If (c) has a solution, what are their speeds at that time? (e) At what time(s), if any, do the cars pass each other (calculate exactly if possible)?

3. A ball is thrown from the top edge of a vertical tower. The initial velocity ?⃗0 of the ball is directed at an angle of 60° above the horizontal. The ball is in flight for 6.50 s and hits the ground 15.0 m from the base of the tower. Ignore air resistance and assume the ground is flat at the base of the tower. (a) Draw a sketch showing the tower and the trajectory of the ball from the tower to the ground. (b) What is the initial speed |?⃗0 | of the ball? (c) How high off the ground is the top of the tower. (d) What is the speed |?⃗??????| of the ball just before it hits the ground? (e) What is the angle of the velocity of the ball ?⃗?????? with respect to the horizontal ground just before it hits the ground?

4. 4. You are planning to try out for the soccer team. In the field near your house you practice kicking to improve your technique. On one of your attempts, you kick the ball at an angle of 30o above the horizontal and it strikes a fence 40.0 m away at a point 7.00 m above the level of your kick. a) Draw a sketch below representing this problem. b) Find the initial speed, v0, of the soccer ball. c) Find the magnitude & direction of the velocity, V, of the soccer ball when it strikes the fence. d) Draw a second sketch representing the information you found in part ‘c)’.

Answer 1