1. (26 points) The one–dimensional motion of a skateboard rider is shown below in the graph of the instantaneous velocity v vs. t. Assume for the purposes of this problem that the positive direction of motion is rightward along the x-axis.

  1. (1 point) What direction is the rider moving between 0 and 4 seconds, rightward or leftward?
  2. (1 point) What direction is the rider moving between 4 and 8 seconds, rightward or leftward?
  3. (1 point) What direction is the rider moving between 8 and 13 seconds, rightward or leftward?
  4. (1 point) What direction is the rider moving between 13 and 20 seconds, rightward or leftward?
  5. (2 points) At what times does rider the come to a stop?
  6. (3 points) Sketch the acceleration a of the rider on the axes below the v vs t curve. Label the vertical a axis with the correct values of the accelerations in the appropriate time intervals, which are aligned with the times for the v vs t curve.
  7. (17 points) Calculate the average velocity of the rider between 0 and 20 seconds. Show all steps. Write clearly, carefully and neatly. Box your answer. Thanks.





 

2. (20 points) A rescue package is dropped from a hovering helicopter with initial speed zero and falls downward for a distance of 200 m. After falling the 200 m, it reaches a velocity V2 when a timed parachute opens and the acceleration becomes zero. It falls a distance H = 100 m with this zero acceleration. Then it hits the surface of a lake and decelerates (slows down) with an acceleration of magnitude 8.0 m/s2 . As you can see, the acceleration points up while it is in the water.


Show all steps. Write clearly, carefully and neatly. Box your answer. Thanks.
(a) (10 points) What distance D below the water surface does the package travel before coming momentarily to rest ?

(b) (10 points) What is the average velocity for the entire trip from the initial drop point to the point where it comes momentarily to rest?

3. ( 20 points) The 4 vectors are oriented as shown in the figure below.

Both the vector-A and the vector-B have related angles of 60 degrees with the x-axis.

Find:

(a) (7 points) the x and y components Rx and Ry of the resultant vector given by:

(b) (6 points) The magnitude R of the resultant vector.
(c) (7 points) The direction of the resultant vector. What is the related angle with the x-axis? In what quadrant does the resultant vector point? Make a sketch of the resultant on the axes provided. Show the related angle in the sketch.

  1. Extra Credit (6 points) A prospective Raider on try-out must kick a football from a point 36.0 m from the goal. The ball must clear a cross-bar that is 3.05 m high at the goal point. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53 0 to the horizontal.

    2. Does the ball travel above the cross-bar when it passes the goal point? Answer yes or no and prove your answer. (In other words, is y greater than 3.05 m when x = 36.0 m ? Yes or no .)