13.06 Applications of Vectors

A soccer ball is kicked with a velocity of 55 \text{ km/h} and an angle of inclination of 50 \degree.

A force has a magnitude of 78 \text { N} and makes an angle of 27 \degree counterclockwise from the horizontal.

A force has a magnitude of 37 \text { N} and makes an angle of 48 \degree clockwise from the vertical.

Express each of the following forces as a vector in terms of \mathbf{i} and \mathbf{j}:

Express each of the following forces as a vector in component form:

Let forces \overrightarrow{A} and \overrightarrow{B} be as shown in the following diagrams. If C newtons \text { (N)} is the magnitude of the resultant force, calculate C correct to the nearest whole number.

a

b

Two forces, of magnitudes 30 newtons and 26 newtons, are acting on the same object separated by an angle of 140 \degree. If F newtons is the magnitude of the resultant force, calculate F correct to one decimal place.

A 150 \text { N} force is to be resolved into two rectangular components such that the magnitude of one component is 2 times the magnitude of the other.

If a 12 \text { N} force was resolved into two equal rectangular components, find x, the magnitude of each component.

A boat heads directly across a river with a velocity of 13 \text{ m/s}. If the river flows at 4\text{ m/s} in the opposite direction, find the boat's resultant velocity.

A box is at rest on a ramp that is inclined at an angle of 12 \degree. It is being held at rest by a 2134 \text { N} force perpendicular to the ramp and a 454 \text { N} force of friction parallel to the surface of the ramp. Find the weight of the box to the nearest tenth of a newton.

A pair of wet jeans is hanging from the middle of a clothes line. The pair of jeans weighs 40 \text { N} and the ends of the clothes line are at 16 \degree below the horizontal.

A chandelier with a weight of 310 \text { N} is hanging from two chains nailed to the ceiling at angles of 61\degree and 68 \degree respectively.

A decoration weighing 40 \text { N} is hanging from two ropes of equal length that are attached to the ceiling. If the angle between the ropes is 140 \degree, find \left|\mathbf{T}\right|, the magnitude of the tension in each rope. Round your answer to the nearest newton.

A wooden crate weighing 1500 \text { N} is hanging from three 8 \text { m} chains attached to the ceiling of a warehouse at three points that form an equilateral triangle with a side length of 12 \text { m}. Find \left|\mathbf{T}\right|, the tension in each chain.

An object weighing 75 \text { N} is on a ramp that is inclined at 17 \degree. It is held at rest by two rectangular components: a force \mathbf{P} perpendicular to the ramp and a friction force \mathbf{F} parallel to the ramp.

A car weighing 19\,000 \text { N} is kept from rolling down an inclined road by a force applied at an angle of 7 \degree to the road. If the road is at an angle of 7 \degree to the horizontal, what is the magnitude of the force? Round your answer to the nearest Newton.

Find the acceleration of a 40 \text { kg} object as it slides down a ramp inclined at 11 \degree to the horizontal if there is no friction. Assume the acceleration due to gravity is 9.8 \text{ m/s}^2and Round your answer to one decimal place.

A car travelling north collides with a car travelling east. The resultant momentum after the collision is 36\,000 \text{ kg} \bullet \text{m/s N } 60 \degree \text{E} .

A ship is 30 \text { km} at a bearing of \text{N }50.7 \degree \text{E} from a lighthouse.

A 17 \text { kg} photo frame is hung on a wall with a string attached to its top-left and top-right corners. The middle of the string is placed on a nail on the wall, and the angle between each half of the string and the horizontal is 45 \degree. Find \left|\mathbf{T}\right|, the magnitude of the tension in each half of the string, to the nearest tenth of a Newton. Assume the acceleration due to gravity is 9.8 \text{ m/s}^2.

Mahmoud is pulling a 90 \text { kg} esky with a rope that is at 30 \degree with the ground. The force he is applying has a horizontal component of 112 \text { N}. What is the total force that he is applying? Round your answer to the nearest Newton.

A 220 \text { N} force is resolved into the components 120\text { N} and 160\text { N}. Are these components rectangular?

A lamp with a mass of 4 \text { kg} is hanging from a rope attached to the ceiling.

An object with a mass of 7\text { kg} is on a ramp that is inclined at 27 \degree. It is held at rest by two rectangular components: a force \mathbf{P} perpendicular to the ramp and a friction force \mathbf{F} parallel to the ramp. Assume the acceleration due to gravity is 9.8 \text{ m/s}^2.