91Ó°ÊÓ

Solve the given problems. Use a ruler and protractor as in Examples 6 and 7. A driver takes the wrong road at an intersection and travels \(4 \mathrm{mi}\) north, then 6 mi east, and finally 10 mi to the southeast to reach the home of a friend. What is the displacement of the friend's home from the intersection?

Solve the given problems. Use a ruler and protractor as in Examples 6 and 7. A ship travels \(20 \mathrm{km}\) in a direction of \(30^{\circ}\) south of east, then turns and goes due south for another \(40 \mathrm{km}\), and finally turns again \(30^{\circ}\) south of east and goes another \(20 \mathrm{km}\). What is the ship's displacement from its original position?

Solve the given problems. Use a ruler and pro- tractor as in Examples 6 and 7. A ship travels \(20 \mathrm{km}\) in a direction of \(30^{\circ}\) south of east, then turns and goes due south for another \(40 \mathrm{km},\) and finally turns again \(30^{\circ}\) south of east and goes another \(20 \mathrm{km}\). What is the ship's displacement from its original position?

Solve the given problems. Use a ruler and protractor as in Examples 6 and 7. Three ropes hold a helium-filled balloon in place, but two of the ropes break. The remaining rope holds the balloon with a tension of \(510 \mathrm{N}\) at an angle of \(80^{\circ}\) with the ground due to a wind. The weight (a vertical force) of the balloon and contents is \(400 \mathrm{N},\) and the upward buoyant force is 900 N. The wind creates a horizontal force of \(90 \mathrm{N}\) on the balloon. What is the resultant force on the balloon?

Solve the given problems. Use a ruler and protractor as in Examples 6 and 7. While unloading a crate weighing \(610 \mathrm{N},\) the chain from a crane supports it with a force of \(650 \mathrm{N}\) at an angle of \(20^{\circ}\) from the vertical. What force must a horizontal rope exert on the crate so that the total force (including its weight) on the crate is zero?