A rock is thrown vertically upward with a speed of 12.0m/s. Exactly 1.00s later, a ball is thrown up vertically along the same path with a speed of 18.0m/s. (a) At what time will they strike each other

Ok, remember that the only force acting on the objects will be the acceleration force.

First, let's describe the motion of the rock.

The acceleration will be:

Ar(t) = -9.8m/s^2

(where the negative sign is because the gravity pulls the rock downwards).

If we want to obtain the velocity of the rock, we should integrate over time and get:

Vr(t) = (-9.8m/s^2)*t + v0

Where v0 is the initial velocity, and we know that it is:

v0  = 12.0m/s

Then:

Vr(t) = (-9.8m/s^)*t + 12m/s.

And the position can be obtained if we integrate again.

Pr(t) =  (-4.9m/s^)*t^2 + 12m/s*t + p0

Where p0 is the initial position.

Now let's do the same for the ball, but the ball is thrown one second after, so we will work with the variable (t - 1s)

Ab(t) = -9.8m/s^2

Vb(t) = (-9.8m/s^2)*(t - 1s) + 18m/s

Pb(t) =  (-4.9m/s^2)*(t - 1s)^2 + 18m/s*(t - 1s) + p0

As the ball is thrown along the same path than the rock, the initial position is the same in both cases.

Now the two objects will impact each other when:

Pb(t) = Pr(t)

(-4.9m/s^2)*(t - 1s)^2 + 18m/s*(t - 1s) + p0 =  (-4.9m/s^)*t^2 + 12m/s*t + p0

Let's solve this for t.

(-4.9m/s^2)*(t - 1s)^2 + 18m/s*(t - 1s) =  (-4.9m/s^)*t^2 + 12m/s*t

(-4.9m/s^2)*(t^2 -2*t*1s +  1s^2) + 18m/s*(t - 1s)  =  (-4.9m/s^)*t^2 + 12m/s*t

(-4.9m/s^2)*(-2*t*1s + 1s^2) + 18m/s*t - 18m = 12m/s*t

-4.9m + 9.8m/s*t + 18m/s*t  - 18m = 12m/s*t

-22.9m = t*(12m/s - 9.8m/s - 18m/s)

22.9m = t*16.8m/s

(22.9/16.8)s = 1.363 s

So the ball and the rock will strike each other at t = 1.363 seconds.

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.

there is no correct list among the choices you've provided.

the list might look something like this:

-- baby human

-- piccolo

-- flute

-- soprano singer

-- trumpet

-- tenor singer

-- trombone

-- baritone singer

-- baritone horn

-- bass singer

-- tuba

since i had to make up the list myself, i made it easy on myself, and i didn't try to shuffle the string instruments and woodwinds into it too.