91Ó°ÊÓ

A plane is flying with an airspeed of 160 miles per hour and heading of \(150^{\circ}\). The wind currents are running at 35 miles per hour at \(165^{\circ}\) clockwise from due north. Use vectors to find the true course and ground speed of the plane.

Find the work performed when the given force \(\mathbf{F}\) is applied to an object, whose resulting motion is represented by the displacement vector d. Assume the force is in pounds and the displacement is measured in feet. \(\mathbf{F}=-67 \mathbf{i}+39 \mathbf{j}, \mathbf{d}=-96 \mathbf{i}-28 \mathbf{j}\)

The problems that follow review material we covered in Section 6.4. Eliminate the parameter \(t\) and graph the resulting equation. $$ x=3+2 \sin t, y=1+2 \cos t $$

Find the magnitude of each of the following vectors. $$\mathbf{U}=5 \mathbf{i}+12 \mathbf{j}$$

Find the work performed when the given force \(\mathbf{F}\) is applied to an object, whose resulting motion is represented by the displacement vector d. Assume the force is in pounds and the displacement is measured in feet. \(\mathbf{F}=-6 \mathbf{i}+19 \mathbf{j}, \mathbf{d}=8 \mathbf{i}+55 \mathbf{j}\)

The problems that follow review material we covered in Section 6.4. Eliminate the parameter \(t\) and graph the resulting equation. $$ x=\cos t-3, y=\sin t+2 $$

Find the magnitude of each of the following vectors. $$\mathrm{U}=20 \mathrm{i}-21 \mathrm{j}$$

A plane is flying with an airspeed of 244 miles per hour with heading \(272.7^{\circ}\). The wind currents are running at a constant \(45.7\) miles per hour in the direction \(262.6^{\circ}\). Find the ground speed and true course of the plane.

Find the work performed when the given force \(\mathbf{F}\) is applied to an object, whose resulting motion is represented by the displacement vector d. Assume the force is in pounds and the displacement is measured in feet. \(\mathbf{F}=85 i, \mathbf{d}=6 i\)

A plane has an airspeed of 195 miles per hour and a heading of \(30.0^{\circ}\). The ground speed of the plane is 207 miles per hour, and its true course is in the direction of \(34.0^{\circ}\). Find the speed and direction of the air currents, assuming they are constants.