Vector Applications

1. Feb 9, 2006

Huskies213

Can anyone explain what to do for these 2 ?

1.) If a=3i-4j, and b=4i-3j, what is the magnitude of the vector a-b?

2.) A boy throws a ball at an initial velocity of 26m/s at an angle of 20 degrees above the horizontal. How high above the projection point is the ball after 1.4 seconds ?

2. Feb 9, 2006

Staff: Mentor

For the vector problem, i,j represent usually represent mutually orthogonal (perpendicular) vectors, e.g. in x,y-directions.

To add two vectors, one adds corresponding components.

let a = a1i + a2j, and b = b1i + b2j, so a + b = (a1+b1)i + (a2+b2)j. The subtraction is just the additive inverse, i.e. replace + with -.

The magnitude of a is just sqrt(a12+a22). Remember the formula for the length of the hypotenuse of a right triangle - Pythagorean theorem.

In question 2, one has to resolve the vector given by "26m/s at an angle of 20 degrees" into horizontal and vertical components. The ball travels vertically with some velocity component, but decelerates due to gravity, reaches a maximum at some time T, and returns to the same initial elevation at time 2T (i.e. T up and T down - neglecting air resistance).

Using the vertical velocity component, one can establish the equation of motion as a function of time to determine where the ball is at 1.4 s. If T (time to max height) < 1.4 s, then the ball is falling back from its maximum altitude.