In the following figure, the magnitudes of the vectors are \(|\vec{a}| = 8\) and \(|\vec{b}| = 4.5\text{.}\) Assume that \(\vec{c} = \vec{a} + \vec{b}\) and \(\vec{d} = \vec{a} - \vec{b}\text{.}\)
Figure1.11.1.Two vectors.
Determine the magnitude of the vectors \(\vec{c}\) and \(\vec{d}\text{?}\) What is the angle to each vector from the positive \(x\)-axis?
In the following figure, the magnitudes of the vectors are \(|\vec{a}| = 5\) and \(|\vec{b}| = 5\text{.}\) Assume that \(\vec{c} = \vec{a} + \vec{b}\) and \(\vec{d} = \vec{a} - \vec{b}\text{.}\)
Figure1.11.2.Two vectors.
Determine the magnitude of the vectors \(\vec{c}\) and \(\vec{d}\text{?}\) What is the angle to each vector from the positive \(x\)-axis?
Three vectors add together to equal \(0\text{.}\) One vector has magnitude \(3\) and points in the positive \(x\)-direction; a second vector has magnitude \(5\) and points at \(120^o\) from the positive \(x\)-axis. Determine the third vector as a magnitude and direction.
Calculation1.11.4.Sums and Differences of Vectors.
Use the figure to determine a single vector that is equivalent to the given summation of vectors in each of the cases below. (The notation \(\vec{PQ}\) represents a vector pointing from point \(P\) to point \(Q\text{.}\))
A kicker punts a football from the very center of the field to the sideline \(42\) yards downfield. What is the magnitude of the net displacement of the ball in yards?
A certain flying saucer is initially located at a position \(\vec{r}_i = 400 \hat{x} + 350 \hat{y} \mathrm{~m}\text{.}\) After a few minutes it has moved to a location \(\vec{r}_f = 650 \hat{x} - 800 \hat{y} \mathrm{~m}\text{.}\) What is the displacement of the flying saucer?
A park has a circular pond with a radius of \(100 \mathrm{~m}\text{.}\) Benny starts at its westernmost point, then waddles counterclockwise around the pond until he is at its northernmost point. What is the magnitude and direction of Benny’s change in position?
