Add vectors at best angles with a mix of pythagorean theorem for magnitude…

r=√(x2+y2)r=√<(19,600m)2+(4,900m)2>r=20,200m |

and tangent for direction.

You are watching: Vector components vector resolution and vector addition answers

tanθ= | y | = | 4,900m | |

x | 19,600m | |||

θ= | 14.04° | |||

Don"t forget come answer the question.

The target of the laser beam is 20,200m far at an angleofelevationof14.04°.

Oh yeah, and also don"t forget to make a drawing. I most likely should have actually told friend to carry out that earlier. I feel poor that I"ve done that double in the part on vectors. Ns should set a much better example. Let me do it approximately you by providing you an man drawing.

If you have actually a feeling of déjàvu, do not it is in alarmed. The matrix is fine. Ns recycled the equipment to this difficulty from an previously one. The idea was to present a usual problem solving technique used in benidormclubdeportivo.org. Whenever possible, take a complicated problem the you haven"t solved and reduce it one that you have solved.

How walk one include parallel vectors? basic — add them. Just how does one add antiparallel vectors? Also simple — subtract them. Just how does one add vectors at best angles. Reasonably simple — usage pythagorean theorem and tangent. How does one include vectors the aren"t at 0°, 180°, or 90°? Brutally simple — deal with them right into components. Don"t permit the vectors do you occupational harder. Do them point in a direction that"s practically for you. Do them in much easier vectors.

And then the student learned the there really was no such point as a "bad" vector and everyone lived happily ever after. The End.

### practice difficulty 2

Three pressures act top top a point: 3N at 0°, 4N in ~ 90°, and also 5N at 217°. What is the network force?

solution

Resolve the vectors right into their materials along the x and y axes. (Watch the signs.) Then add the contents along each axis to obtain the materials of the resultant. Use these to get the magnitude and direction of the resultant. Troubles with a lot of materials are simpler to occupational on as soon as the values room written in table type like this…

magnitudedirectionx-componenty-componentfirst force | 3N | 0° | +3N | 0 N |

second force | 4N | 90° | 0N | +4N |

third force | 5N | 217° | −4N | −3N |

resultant | 1.4N | 135° | −1N | +1N |

A drawing or animation may be helpful.

### practice difficulty 3

A cyclist top due west on a straight road. The wind is blowing native 248° in ~ 10m/s.Is this wind much more like a headwind or a tailwind?What is the headwind/tailwind speed?What is the crosswind speed?

solution

Start with a diagram. You might draw a height view the this cyclist choose I did, but it isn"t necessary. Do draw an arrow pointed to the right, however, to stand for the direction of the cyclist. Wind directions room measured clockwise native due north. North is 0°, eastern is 90°, south is 180°, and also west is 270°. The wind is coming from 248°, which lies somewhere in between south and west. Attract an arrowhead from the lower left edge to the upper right corner to represent the wind. The angle between the 2 arrows is…

270°− 248°=22°

Add this info to the diagram.

This is why you need a diagram. It provides it basic to view the answer. This wind is much more like a headwind than a tailwind.

The headwind is provided by the "x" component.

vx=vcosθvx=(10m/s)cos(22°)vx=9.2m/s |

The crosswind is provided by the "y" component.

vy=vsinθvy=(10m/s)sin(22°)vy=3.7m/s |

### practice problem 4

One unfortunate winter day I happened to on slide on one icy ramp lean 37° come the horizontal. Discover my acceleration under the ramp provided that the acceleration because of gravity points straight down and also has a worth of 9.8m/s2. (Assume the ice is perfect frictionless.)

solution

This is an example of one inclined airplane problem — something usual in introductory benidormclubdeportivo.org classes. Solution…

Start through a diagram. Attract a diagonal heat to stand for the ramp. Draw a tilted box to represent negative unfortunate me. Attract an arrowhead pointing down and also label it g because that acceleration as result of gravity.

I can"t accelerate *down* in this problem because the solid surface of the ramp is in the way, but I can accelerate *down the ramp*; the is, parallel come the ramp. This sets a organic direction because that a rotated coordinate system.

x′ | parallel come the surface |

y′ | perpendicular come the surface |

Add the rotated name: coordinates axes to the drawing, then task the acceleration vector onto them. (I"ve drawn this with dashed lines.) with a small bit that geometric reasoning, it deserve to be displayed that the angle between a horizontal line and the parallel axis (also well-known as the edge of inclination) is equal to the angle between a upright line and also the perpendicular axis. That provides us a best triangle with the complying with sides…

g | hypotenuse |

gx′ | oppositeside |

gy′ | adjacentside |

which means…

gx′ | =gsinθ |

gy′ | =gcosθ |

Adding this details to the diagram puts every little thing in perspective.

We just care about the ingredient parallel come the ramp, therefore we"ll only do one calculation.

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gx′=9.8m/s2sin37°=5.9m/s2

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