NY Regents June 2008, Part 4
 61. The diagram in your answer booklet represents a transverse wave moving on a uniform rope with point A labeled as shown. On the diagram in your answer booklet, mark an X at the point on the wave that is 180° out of phase with point A.

 Base your answers to questions 62 through 64 on the information below.   A kicked soccer ball has an initial velocity of 25 meters per second at an angle of 40.° above the horizontal, level ground. [Neglect friction.]   62. Calculate the magnitude of the vertical component of the ball’s initial velocity. [Show all work, including the equation and substitution with units.]

 63. Calculate the maximum height the ball reaches above its initial position. [Show all work, including the equation and substitution with units.]

 64. On the diagram in your answer booklet, sketch the path of the ball’s flight from its initial position at point P until it returns to level ground.

 Base your answers to questions 65 through 67 on the information and diagram below.   A 15-ohm resistor, R1, and a 30.-ohm resistor, R2, are to be connected in parallel between points A and B in a circuit containing a 90.-volt battery.       65. Complete the diagram in your answer booklet to show the two resistors connected in parallel between points A and B.

 66. Determine the potential difference across resistor R1.

 67. Calculate the current in resistor R1. [Show all work, including the equation and substitution with units.]

 Base your answers to questions 68 through 71 on the information and data table below.   The spring in a dart launcher has a spring constant of 140 newtons per meter. The launcher has six power settings, 0 through 5, with each successive setting having a spring compression 0.020 meter beyond the previous setting. During testing, the launcher is aligned to the vertical, the spring is compressed, and a dart is fired upward. The maximum vertical displacement of the dart in each test trial is measured. The results of the testing are shown in the table below.   68. Plot the data points for the dart’s maximum vertical displacement versus spring compression.

 69. Draw the line or curve of best fit.

 70. Using information from your graph, calculate the energy provided by the compressed spring that causes the dart to achieve a maximum vertical displacement of 3.50 meters. [Show all work, including the equation and substitution with units.]

 71. Determine the magnitude of the force, in newtons, needed to compress the spring 0.040 meter.

 Base your answers to questions 72 through 74 on the information and diagram below.   A ray of monochromatic light having a frequency of 5.09 × 1014 hertz is incident on an interface of air and corn oil at an angle of 35° as shown. The ray is transmitted through parallel layers of corn oil and glycerol and is then reflected from the surface of a plane mirror, located below and parallel to the glycerol layer. The ray then emerges from the corn oil back into the air at point P.     72. Calculate the angle of refraction of the light ray as it enters the corn oil from air. [Show all work, including the equation and the substitution with units.]

 73. Explain why the ray does not bend at the corn oil-glycerol interface.

 74. On the diagram in your answer booklet, use a protractor and straightedge to construct the refracted ray representing the light emerging at point P into air.

 Base your answers to questions 75 and 76 on the information and data table below.   In the first nuclear reaction using a particle accelerator, accelerated protons bombarded lithium atoms, producing alpha particles and energy. The energy resulted from the conversion of mass into energy. The reaction can be written as shown below.     75. Determine the difference between the total mass of a proton plus a lithium atom (), and the total mass of two alpha particles (), in universal mass units.

 76. Determine the energy in MeV (megaelectronvolts) produced in the reaction of a proton with a lithium atom.