Answer:
- 1.07 ft
Explanation:
V1 = (-5, 7, 2)
V2 = (3, 1, 2)
Projection of v1 along v2, we use the following formula
=\frac{\overrightarrow{V1}.\overrightarrow{V2}}{V2}
So, the dot product of V1 and V2 is = - 5 (3) + 7 (1) + 2 (2) = -15 + 7 + 4 = -4
The magnitude of vector V2 is given by
= 
So, the projection of V1 along V2 = - 4 / 3.74 = - 1.07 ft
Thus, the projection of V1 along V2 is - 1.07 ft.
so we need to find the direction of v2
To answer, evaluate the power of 10 in the given choices. If it is positve, move the decimal n places to the right. If it is negative, move the decimal n corresponding places to the left. From all the choices given, only the choices D, E, and F will give us the correct answer.
Answer: 996m/s
Explanation:
Formula for calculating velocity of wave in a stretched string is
V = √T/M where;
V is the velocity of wave
T is tension
M is the mass per unit length of the wire(m/L)
Since the second wire is twice as far apart as the first, it will be L2 = 2L1
Let V1 and V2 be the speed of the shorter and longer wire respectively
V1 = √T/M1... 1
V2 = √T/M2... 2
Since V1 = 249m/s, M1 = m/L1 M2 = m/L2 = m/2L1
The equations will now become
249 = √T/(m/L1) ... 3
V2 = √T/(m/2L1)... 4
From 3,
249² = TL1/m...5
From 4,
V2²= 2TL1/m... 6
Dividing equation 5 by 6 we have;
249²/V2² = TL1/m×m/2TL1
{249/V2}² = 1/2
249/V2 = (1/2)²
249/V2 = 1/4
V2 = 249×4
V2 = 996m/s
Therefore the speed of the wave on the longer wire is 996m/s
Kinetic energy is never negative, but potential energy can be.
Potential energy depends on height above some reference level,
and you can pick any level you want as the reference. So, if the
object is below the reference level you pick, then its potential
energy relative to your reference level is negative.
What that means is: You have to lift it / do work on it / give it more
energy than it has now ... in order to move it to the reference level.
(That's exactly the situation with electrons bound to an atom. Their
energy is considered negative, because we have to do work and
give them more energy to rip them away from the atom.)
_____________________________________
Regarding the other choices:
-- Kinetic energy is scalar ... Yes. So is potential energy.
-- Kinetic energy increases with height ...
No. It doesn't, but potential energy does.
-- Kinetic energy depends on position ...
No. It doesn't, but potential energy does.
