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Physics Problems (Displacement Vectors; Velocities etc.)

I would like you to show me all of your work/calculations and the correct answer to each problem.

13. A ball rolls at a constant velocity of 1.50 m / s at an angle of 45 degrees below the + x-axis in the fourth quadrant. If we take the ball to be at the origin at t = 0, what are its coordinates (x, y) 1.65 s later?

Answers: x = 1.75 m; y = -1.75 m

29. Consider yourself to be in boat A traveling along straight path on a lake with a speed of v = 30 km / h. Another boat, boat B, travels at a speed of v = 45 km / h.
A B

Find the difference of the velocities, v = v - v
BA B A

When (a) the other boat travels in the same direction in front of you and (b) the other boat is approaching you from the opposite direction.

Answers: (a) +15 km / h, (b) -75 km / h

33. A airplane flies northwest for 250 mi and then west for 150 mi. Find the resultant (or sum) displacement vector by (a) the graphical method and (b) the component method.

Answers: (b) 372 mi at 28.4 degrees north of west

65. A swimmer maintains a speed of 0.15 m / s relative to the water he swims directly toward the opposite shore of a river. The river has a current that flows at 0.75 m /s. (a) How far downstream is he carried in 1.5 min? (b) What is his velocity relative to an observer on shore?

Answers: (a) 68 m, (b) 0.76 m / s, 11 degrees relative to shore.

87. An arrow has an initial launch speed of 18 m / s. If it must strike a target 31 m away at the same elevation, what should be the projection angle?

Answer: 35 degrees or 55 degrees

89. A stone thrown off a bridge 20 m above a river has an initial velocity of 12 m / s at an angle of 45 degrees above the horizontal. (a) What is the range of the stone? (b) At what velocity does the stone strike the water?

Answers: (a) 26 m, (b) 23 m / s at 68 degrees below horizontal.

93. A quarterback passes a football - at a velocity of 50 ft / s at an angle of 40 degrees to the horizontal - toward an intended receiver 30 yd downfield. The pass is released 5.0 ft above the ground. Assume that the receiver is stationary and that he will catch the ball if it comes to him. Will the pass be completed? If not, will the throw be long or short? Show your work.

99. You are traveling and start out 200 mi directly south of your destination. If you first go 150 mi at 25 degrees west of north to visit your friends, what must be your second displacement in order for you to get to your destination?

Answer: 90 miles at 45 degrees north of east.

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