Problem 1
For each of the following quantities, indicate whether it is a scalar or a vector: (a) the time it takes you to run the \(100-m\) dash, (b) your displacement after running the \(100-\mathrm{m}\) dash, (c) your average velocity while running, (d) your average speed while running.
Problem 1
Check For each of the following quantities, indicate whether it is a scalar or a vector: (a) the time it takes you to run the \(100-\mathrm{m}\) dash, (b) your displacement after running the \(100-\mathrm{m}\) dash, (c) your average velocity while running, (d) your average speed while running.
Problem 3
(a) If the angle of the chair lift is decreased, will the horizontal distance \(d_{x}\) increase, decrease, or stay the same? Assume that the length of the lift remains the same, \(d=190 \mathrm{~m}\). (b) Find \(d_{x}\) for the angle \(\theta=15^{\circ}\).
Problem 5
Find the \(x\) and \(y\) components of a position vector that has a magnitude of \(r=75.0 \mathrm{~m}\) and an angle relative to the \(x\) axis of (a) \(35.0^{\circ}\) and (b) \(65.0^{\circ}\).
Problem 6
Challenge The press box at a baseball park is \(9.75 \mathrm{~m}\) above the ground. A reporter in the press box looks at an angle of \(15.0^{\circ}\) below the horizontal to see second base. What is the horizontal distance from the press box to second base?
Problem 6
The press box at a baseball park is \(9.75 \mathrm{~m}\) above the ground. A reporter in the press box looks at an angle of \(15.0^{\circ}\) below the horizontal to see second base. What is the horizontal distance from the press box to second base?
Problem 7
(a) If the horizontal distance is doubled but the vertical rise remains the same, will the angle \(\theta\) increase, decrease, or stay the same? (b) Calculate \(\theta\) for \(d_{x}=2(1.33 \mathrm{~m})=2.66 \mathrm{~m}\) and \(d_{y}=0.380 \mathrm{~m}\).
Problem 8
A road that rises \(1 \mathrm{ft}\) for every \(100 \mathrm{ft}\) traveled horizontally is said to have a 1\% grade. Portions of the Lewiston grade, near Lewiston, Idaho, have a \(6 \%\) grade. At what angle is this road inclined above the horizontal?
Problem 9
You slide a box up a loading ramp that is \(3.7 \mathrm{~m}\) long. At the top of the ramp the box has risen a height of \(1.1 \mathrm{~m}\). What is the angle of the ramp above the horizontal?
Problem 10
What distinguishes a vector from a scalar?
