91Ó°ÊÓ

The force vectors given are acting on a common point \(P\). Find an additional force vector so that equilibrium takes place. \(\mathbf{F}_{1}=\langle-2,7\rangle ; \mathbf{F}_{2}=\langle 5,3\rangle\)

Solve each triangle using the law of sines. If the law of sines cannot be used, state why. Draw and label a triangle or label the triangle given before you begin. $$ \begin{aligned} \text { side } b &=385 \mathrm{~m} \\ \angle B &=47^{\circ} \\ \angle A &=108^{\circ} \end{aligned} $$

Solve each triangle using the law of sines. If the law of sines cannot be used, state why. Draw and label a triangle or label the triangle given before you begin. side \(b=10 \sqrt{3}\) in. $$ \begin{aligned} &\angle A=30^{\circ} \\ &\angle B=60^{\circ} \end{aligned} $$

Solve each of the following equations for the unknown part. $$ b^{2}=3.9^{2}+9.5^{2}-2(3.9)(9.5) \cos 30^{\circ} $$

For each position vector given, (a) graph the vector and name the quadrant, (b) compute its magnitude, and (c) find the acute angle \(\theta\) formed by the vector and the nearest \(x\)-axis. $$ \langle-7,6\rangle $$

The range of a projectile: \(R=\frac{v^{2} \sin \theta \cos \theta}{16}\) The range of a projected object (total horizontal distance traveled) is given by the formula shown, where \(v\) is the initial velocity and \(\theta\) is the angle at which it is projected. If an arrow leaves the bow traveling \(175 \mathrm{ft} / \mathrm{sec}\) at an angle of \(45^{\circ}\), what horizontal distance will it travel?

For each pair of vectors \(u\) and \(v\) given, compute (a) through (d) and illustrate the indicated operations graphically. a. \(\mathbf{u}+\mathbf{v}\) b. \(\mathbf{u}-\mathbf{v}\) c. \(2 \mathbf{u}+1.5 \mathbf{v}\) d. \(\mathbf{u}-2 \mathbf{v}\) $$ \mathbf{u}=\langle-5,-3\rangle ; \mathbf{v}=\langle 6,-4\rangle $$

Force vectors: For the force vector \(\mathbf{F}\) and vector \(\mathbf{v}\) given, find the amount of work required to move an object along the entire length of \(v_{.}\)Assume force is in pounds and distance in feet. $$\mathbf{F}=\langle 15,10\rangle ; \mathbf{v}=\langle 50,5\rangle$$

Find comp,u for the vectors \(u\) and \(v\) given. $$\mathbf{u}=8 \mathrm{i} ; \mathbf{v}=10 \mathbf{i}+3 \mathbf{j}$$

A UFO is sighted on a direct line between the towns of Batesville and Cave City, sitting stationary in the sky. The towns are \(13 \mathrm{mi}\) apart as the crow flies. A student in Batesville calls a friend in Cave City and both take measurements of the angle of elevation: \(35^{\circ}\) from Batesville and \(42^{\circ}\) from Cave City. Suddenly the UFO zips across the sky at a level altitude heading directly for Cave City, then stops and hovers long enough for an additional measurement from Batesville: \(24^{\circ}\). If the UFO was in motion for \(1.2 \mathrm{sec}\), at what average speed (in mph) did it travel?