Physics Chapter 3 Test

subtraction of vectors

-a minus sign of a vector tells direction; the magnitude is always positive -changes direction by 180°

vector components

-horizontal and vertical components -perpendicular V=Vx + Vy Vy=Vsinθ Vx=Vcosθ

scalar components

A=Axi + Ayj

If two vectors are given such that A + B = 0, what can you say about the magnitude and direction of vectors A and B?

Same magnitude, must be in opposite direction

projectile

an object moving in 2D under influence of gravity -horizontal velocity is constant -constant vertical acceleration (g)

A small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air as it moves. After it is fired, what happens to the ball?

it falls right back into the cart

parallelogram method

two vectors are drawn from a common origin, and a parallelogram is construced using the vectors as adjacent sides

Angled Launch

-if an object is launched at an initial angle of θ₀ w/horizontal, the analysis is similar except V₀ has horizontal and vertical components -initial velocity: Vx=V₀cosθ, Vy=V₀sinθ

Horizontal Launch

-if an object is launched horizontally, initial velocity (Vy₀)=0 -initial velocity (V₀)=horizontal velocity (Vx) -vertical motion of dropped=vertical motion of horizontally launched

multiplication of vectors

-product has same direction as the vector and has magnitude of the two multiplied together -if scalar is negative, the magnitude of product is still +, but diretion is opposite of vector →changes vector by 180°

Horizontal Range

-trajectory depends on initial velocity and angle -greatest distance is achieved by using angle close to 45˚ -range (horizontal distance) depends on horizontal speed of ball and on time the ball spends in air because... distance=speed x time and ∆x=Vx∆t -for shallow angles→Vx>Vy₀. Ball doesn't go high, distance short, time short -for steep angles→Vy₀>Vx. Ball goes high and spends longer in air, but doesn't travel far -45˚ angle, Vyo=Vx. In air longer than low angles, greater Vx than high angles

What does a trajectory look like?

-velocity at any point in time found by adding verticaly component of velocity to the horizontal component of velocity -Vy is constant -magnitude of Vx increases -combo of motion produce parabolic curve

Steps to Adding Vectors Using Components

1.) Draw rough tail-to-tip diagram and figure out quadrant 2) Resolve each factor into horizontal and vertical components 3) Add components to find horizonal and vertical components of resultant Rx=Ax+Bx; Ry=Ay+By 4) To find magnitude and direction of vector: R= √(Rx)²+(Ry)²; θ=tan⁻¹(Ry/Rx) *Add 180˚ if resultant is in 2nd or 3rd quad.

You are adding vectors of length 20 and 40 units. What is the only possible resultant magnitude that you can obtain out of the following choices? 1) 0 2) 18 3) 37 4) 64 5) 100

37 because the minimum resultant will occur when the vectors are going in opposite directions and the resultant is 20. The maximum resultant will occur when the vectors are going in the same direction and the resultant is 60. So the possible resultant has to be in the middle

You drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will:

Remain vertically under the plane while falling because both the plane and the package have the same horizontal velocity at the moment of release. They will maintain this velocity in the x-direction, so they stay aligned.

From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which ball has the greater velocity at ground level?

The fired ball. Both balls have the same vertical velocity when they hit the ground (since they are both acted on by gravity for the same time). However, the "fired" ball also has a horizontal velocity. When you add the two components vectorially, the "fired" ball has a larger net velocity when it hits the ground.

unit vectors

dimensionless vectors with length=1

vectors

quantity with magnitude and direction

scalar

quantity with only magnitude

Given that A + B = C, and that lAl + lBl = lCl , how are vectors A and B oriented with respect to each other?

they are parallel and in the same direction