g Suppose that an escalator raises stationary passengers vertically at a speed of ten feet per second, and the escalator is pointing northeast so its passengers also move northeast at ten feet per second. If a child riding the escalator drops a ball so that it rolls north on the escalator at a speed of 5 feet per second, what is the speed of the ball relative to a stationary observer

v = 14 ft / s, 49.6º north of east

Explanation:

This is a relative velocity problem, let's use subscripts to work

* e for the escalator

* p for ball

velocity is a vector whereby

     v = v_e + v_p

The bold are vector.  An easy way to work with this type of problem is to decompose the velocities into a Cartesian coordinate system, where the x-axis coincides with East and the y-axis with North.

stair speed

              sin 45 = v_{ey} / ve

              cos 45 = v_{ex} / ve

              v_{ey} = go sin 45

               v_{ex} = ve cos 45

              v_{ey} = 10 sin 45 = 7.07 ft / s

               v_{ex} = 10 cos 45 = 7.07 ft / s

the speed of the ball is

                v_p = 5 j ^ ft / s

therefore the speed that the observer sees is

X axis

            vₓ = v_{ex}

             vₓ = 7.07 ft / s

Y axis  

            v_y = v_{ey} + v_p

            v_y = 7.07 + 5

            v_y = 12.07 ft / s

we can give the result in two ways

*      v  = (7.07 i ^ +12.07 j ^) ft / s

* in module and angle form

Let's use the Pythagorean theorem

         v =

         v =

         v = 13.99 ft / s

         v = 14 ft / s

we use trigonometry

        tan θ = vy / vx

        θ = tan⁻¹ v_y / vₓ

        θ = tan⁻¹ 12.07 / 7.07

        θ = 49.6º

in the form of cardinal coordinates they are 49.6º north of east

answer: d. a cme increases the amount of energy in the solar wind

explanation:

coronal mass ejections, also called cmes, are large clouds of plasma and magnetic field that erupt from the sun. only when the cloud is aimed at earth will the cme hit earth and therefore cause impacts. high-speed solar wind streams come from areas on the sun known as coronal holes.

double the distance = divide strength by 4