Could a vector ever be shorter than one of its components? Equal in length to one of its components? Explain.

Answer:

Explanation:

The potential energy associated with a body (m) located at a given height (h) above a reference point is defined as:

At the reference point the potential energy is zero. In this case the body is below the reference point (the ceiling), therefore, the value of h is negative:

For the resistor closest to the battery, drawn vertical in the diagram, I = 8 A and P = 320 watts.

Also, the battery voltage is 40 V.

There isn't enough information included in the picture to fill in any of the missing items for the other two resistors.

Answer:

Explanation:

Given the wave function

y(x,t) = 0.340 sin (15πt − 4πx + π/4)

Generally a wave function is of the form

y(x, t) = A•Sin(wt - kx + θ)

Where

A is amplitude

w is angular frequency

θ is the phase angle

k is the wave number.

Then, comparing this with given wave function

k = 4π, w = 15π and θ = π/4

Speed and direction?

The speed of a wave function can be determined using wave equation

v = fλ

w = 2πf

Then, f = w/2π = 15π/2π = 7.5Hz

Also k = 2π/λ

Then, λ = 2π/k = 2π/4π = 0.5 m

Then,

v = fλ = 7.5 × 0.5

v = 3.75m/s

Direction

Since the time and distance coefficient have opposite sign, for an increasing time interval, the translation will have to increase in the positive direction to nullify the change and maintain the phase. Hence, the wave is traveling in the positive x direction