Vector Word Problems

Related Topics:
Common Core (Vector and Matrix Quantities)
Common Core for Mathematics

Videos, solutions, examples, and lessons to help High School students learn to solve problems involving velocity and other quantities that can be represented by vectors.

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Common Core: HSN-VM.A.3

Word Problems Involving Velocity or Other Forces (Vectors), Example 1
In this problem we do a word problem involving the bearing (direction) of a boat.
A boat is traveling at a speed of 30 mph. The vector that represents the velocity is 15<√2 , −√2>. What is the bearing of the boat?

Word Problems Involving Velocity or Other Forces (Vectors), Example 2.
In this problem we are given the bearing and velocity of a plane and the bearing and velocity of the wind; we want to find out the actual velocity of the plane after taking the wind into consideration.
A plane leaves the airport on the bearing of 45° traveling at 400 mph. The wind is blowing at a bearing of 135° at a speed of 40 mph. What is the actual velocity of the plane?

Word Problems Involving Velocity or Other Forces (Vectors), Example 3.
Here we know the force required to keep a box from sliding down a ramp; we want to know the angle of inclination of the ramp.
A 700 lb force just keeps a 400 lb box from sliding down a ramp. What is the angle of inclination of the ramp?

Vectors: Applications

  1. A ship leaves port on a bearing of 28° and travels 7.5 miles. The ship then turns due east and travels 4.1 miles. How far is the ship from port and what is its bearing?

  2. Two tow trucks are pulling on a truck stuck in the mud. Tow truck #1 is pulling with a force of 635 lbs at a 51° from the horizontal while tow truck #2 is pulling with a force of 592 lbs at a 39° from the horizontal. What is the magnitude and direction of the resultant force?

Word Problem with Vectors
The speed of a powerboat in still water is 35 mi/h. It is traveling on a river that flows directly south at 8 mi/h. At what angle should the boat head upriver in order to travel directly west?

How to solve a physics vector river problem?
In order to get across a river to a dock on time, a boat would have to row 65° upstream at 80km/hr if no current was present. If the current is 25 km/hr, what velocity and direction must the boat travel?

Direction and Speed of a Plane in the Wind Using Vectors
This video explains how to use vectors to determine of far off course a plane would fly and what its relative speed would be in the wind. This is solved using vectors.
An airplane is heading due north at an airspeed of 700 km/h, but there is a wind blowing from the northeast at 60 km/h.
How many degrees off course will the plane fly?
What is the plane’s speed relative to the ground?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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