Physics 163

Unit 3: Motion in Two Dimensions

Problem Set B

Overview:

Problem Set B targets your ability to use basic principles of right triangle trigonometry and vector addition principles to analyze relative velocity problems. Such problems include but are not limited to the motion of a riverboat across a river in the presence of a current. The entire set provides a rigorous workout in the interpretation of word story problems and their representation by a diagram. There are three basic questions associated with riverboat problems; these questions pertain to:

i. determining the magnitude and direction of the resultant velocity

ii. determining the time to cross the river

iii. determining the distance that the riverboat moves downstream

You will need to have a solid grasp of at least four skills or conceptual understandings to be successful on Problem Set B:

1. Vectors are added using a head-to-tail method of vector addition. If the vectors being added are at right angles to each other, then the Pythagorean theorem can be used to determine the magnitude of the resultant vector.
2. If the resultant vector is formed by the addition of two right angle vectors, then the direction of the resultant can be determined using SOH CAH TOA. The result of using SOH CAH TOA is that an angle within a right triangle will be known; this angle can then be converted to a direction using a convention such as the counter-clockwise from East convention.
3. For any constant speed motion along a single direction, the distance traveled is related to the speed of travel and the time by the equation d = v • t.
4. Perpendicular components of motion are independent of each other. An alteration in the east-west motion parameters for an object will have no effect upon the north-south motion parameters.

The above principles and their application to riverboat problems can be reviewed at The Physics Classroom.

View Sample Problem Set.

 Problem Description Audio Link 1 A riverboat problem; determination of the magnitude of the resultant velocity 2 Extension of Problem 1; a riverboat problem; determination of the time to cross the river 3 Extension of Problem 1 and 2; a riverboat problem; determination of the downstream distance traveled by the boat 4 A riverboat problem; determination of the magnitude of the resultant velocity 5 Extension of Problem 4; a riverboat problem; determination of the direction of the resultant velocity 6 Extension of Problem 4; a riverboat problem; determination of the downstream distance traveled by the boat 7 A a relative velocity problem for an airplane; requires a good visual represenation using a diagram and some thoughtful analysis; use of SOH CAH TOA 8 Extension of Problem 7; a relative velocity problem for an airplane; use of Pythagoream theorem 9 A riverboat problem; determination of the downstream distance traveled by the boat 10 A riverboat problem; determination of the time to cross the river

Audio Help for Problem: 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10

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