Physics, Foundation Programme - Problem Solving Exercises 7
Vectors
1.  A car is driven 125.0 km due west, then 65.0 km due south. What is the magnitude of its displacement? Solve this problem both graphically and mathematically.
a: 140.9 km
2.  A hiker walks 4.5 km in one direction, then makes a 45° turn to the right and walks another 6.4 km. What is the magnitude of her displacement?
a: 10.1 km
3.   An ant is crawling on the sidewalk. At one moment, it is moving south a distance of 5.0 mm. It then turns southwest and crawls 4.0 mm. What is the magnitude of the ant's displacement?
a: 8.3 mm
FP Physics - Problem Solving Exercises 7WA
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4.  Find the components of the vector with the initial point PI and terminal point P2. Use these components to write a vector that is equivalent to PI P2.
0
-1
1 0
A: v=<4, 2>
						- 2
						
		.......				
		1				
						
						
■1
-2       -1 0
A: v=<4, -1>
■10       12       3 4 A: v=<-l, -4>
a) P1(4,2);P2(-3,-3)
b) P1(0,-3);P2(0,4)
FP Physics - Problem Solving Exercises 7WA
a: v=<-7, -5> a: v=<0, 7>
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5.  Find the magnitude and direction of each vector. (The direction is the angle which the vector makes with the positive x-axis.)
a) v = (-3,4) a: ||v|| = 5, a = 126.87°
b) v = (6,10) a: ||v|| - 2^34, a = 59.036°
c) v = (20, -40) a: ||v|| = 20\/5, a = 296.57°
6.  A plane is flying at an airspeed of 500 km/h at a heading of 124 °. A wind of 60 km/h is blowing from the west. Find the ground speed of the plane.
A: v=551 km/h, ground heading a. = 120.5°
7.  A person who can row 4.2 km/h in still water wants to row due east across a river. The river is flowing from the north at a rate of 1.4 km/h. Determine the heading of the boat required for the boat to travel due east across the river.
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A: a = 70.529°
8.  Find the magnitude of the force necessary to keep a 1,000-kg car from sliding down a ramp inclined at an angle of 5.6°. Round to the nearest tens of newtons. (The gravitation force acting on the car is 9,807 newtons).
A: F=960 N
9.  A force of 480 newtons keeps an 120-kilogram object from sliding down an inclined ramp (the gravitation force acting on the object is 1177 N). Find the angle of the ramp. Round to the nearest tenth of a degree.
A: a = 24.1°
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10. A 68-kg (gravitation force 667 newtons) box is dragged 5 meters along a level floor. Find the work done if a force of 340 newtons, with a direction angle of 32° is used. Round to the nearest joule.
A: W=1442 J
11. A rope is bing used to pull a box up a ramp that is inclined at 15°. The rope exerts a force of 500 newtons on the box, and the rope makes an angle of 30° with the plane of the ramp. Find the work done in moving the box 7 meters. Round to the nearest joule
a: 3031 joules
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