The town of Calculusville is 95 m above sea level and the town of Vectorville is 178 m above sea level. The two towns are 4.8 km apart along a straight, smooth road. A family decides to move from Calculusville to Vectorville. They pack all their belongings in a trailer hitched to their SUV. The SUV pulls the trailer up the road using a force, in newtons, defined by the vector F = [25 000, 14 000]. a) Find the force drawing the trailer up the hill and the force, perpendicular to the hill, tending to lift it. b) What is the work done by the SUV in pulling the trailer up the hill? c) What is the work done in raising the altitude of the trailer?

**44. The drawing shows a force vector that has a magnitude of 475 new- tons. Find the (a) x, (b) y, and (c) z components of the vector. 54.0° 33.0°

A hiker walks 2.5 miles in a direction 65° West of North, then 3.5 miles in a direction 40° South of West, then 1.5 miles due South. What must be the vector displacement of the hiker during the fourth part of the trip in order for the resultant to be 5.5 miles due West for the entire trip? Drawing a vector diagram or drawing individual vectors will help.

A vector has both a direction and a "magnitude", or length. An example of a vector quantity is the wind, which has both a direction and a strength. What is the magnitude of the vector 32+ -93 +7k?

Two workers are trying to move a heavy crate. One pushes on the crate with a force A, which has a magnitude of 480 newtons and is directed due west. The other pushes with a force B, which has a magnitude of 325 newtons and is directed due north. What is the magnitude of the resultant force A + B applied to the crate? Specify your answer up to one decimal place. Do not include units.

Consider the following vectors: A = 5.2j;  B = -4.1i + 2.5j.  Draw a diagram showing the addition of vectors A and B. (a) Find A + B in the Cartesian (x and y component) form. (b) Find the magnitude of A + B. (c) Find the direction of A + B, expressed as a polar angle. (d) Find 1.5A - 3.2B in the Cartesian (x and y component) form. (e) Find the magnitude of 1.5A - 3.2B. (f) Find the direction of 1.5A - 3.2B, expressed as a polar angle.   Note: New drawing also with solution

Vector  A  has a magnitude of 39.5 units and it points in a direction 310° counterclockwise from the positive x-axis. What are the x- and y-components of  A?

Two vectors are given by a  =  1.5î−4.0ĵ and b  =  −11.9î + 8.1ĵ. What is the magnitude of b? i already found out  magnitude of b is 1.44 but how to calculate the angle between vector b and the positive x-axis?

A vector has a magnitude of 2.8 m and points in a direction that is 135 counterclockwise from the a axis. You may want to review (Page 71).

Vector A⃗  has a magnitude of 9.30 m and is pointing in a direction of 25.0 degrees counterclockwise from the positive x axis. Vector B⃗  has a magnitude of 9.70 m and is pointing in a direction of 140. degrees counterclockwise from the positive x axis. What is A⃗ +B⃗ ? Magnitude: Direction (specify as an angle measured counterclockwise from the positive x axis):