Answer:
9.34 N
Explanation:
First of all, we can calculate the speed of the wave in the string. This is given by the wave equation:

where
f is the frequency of the wave
is the wavelength
For the waves in this string we have:
, since it completes 625 cycles per second
is the wavelength
So the speed of the wave is

The speed of the waves in a string is related to the tension in the string by
(1)
where
T is the tension in the string
is the linear density
In this problem:
is the mass of the string
L = 0.75 m is the its length
Solving the equation (1) for T, we find the tension:

Answer:
If the canoe heads upstream the speed is zero. And directly across the river is 8.48 [km/h] towards southeast
Explanation:
When the canoe moves upstream, it is moving in the opposite direction of the normal river current. Since the velocities are vector (magnitude and direction) we can sum each vector:
Vr = velocity of the river = 6[km/h}
Vc = velocity of the canoe = -6 [km/h]
We take the direction of the river as positive, therefore other velocity in the opposite direction will be negative.
Vt = Vr + Vc = 6 - 6 = 0 [km/h]
For the second question, we need to make a sketch of the canoe and we are watching this movement at a high elevation. So let's say that the canoe is located in point 0 where it is located one of the river's borders.
So we are having one movement to the right (x-direction). And the movement of the river to the south ( - y-direction).
Since the velocities are vector we can sum each vector, so using the Pythagoras theorem we have:
![Vt = \sqrt{(6)^{2} +(-6)^{2} } \\Vt=8.48[km/h]](https://tex.z-dn.net/?f=Vt%20%3D%20%5Csqrt%7B%286%29%5E%7B2%7D%20%2B%28-6%29%5E%7B2%7D%20%7D%20%5C%5CVt%3D8.48%5Bkm%2Fh%5D)
Explanation:
The kinetic energy is said to be possessed due to the motion of the object. An object at rest will have zero kinetic energy and if it is in motion it will have some kinetic energy. The mathematical expression for kinetic energy is given by :
...........(1)
Where
m is the mass of the object
v is the velocity of object
It is clear form expression (1) that the kinetic energy of the object is directly proportional to the mass and velocity of an object.
So, the hypothesis for the mass and kinetic energy can be written as " when the mass of the object increases, its kinetic energy also increases because there exists a direct relationship between the mass and the kinetic energy of the object".
Answer: 250n
Explanation:
The formula for gravitational force is: F = (gMm)/r^2
There are two factors at play here:
1) The mass of the planet 'M'
2) The radius 'r'
We can ignore the small M and the g, they are constants that do not alter the outcome of this question.
You can see that both M and r are double that of earth. So lets say earth has M=1 and r=1. Then, new planet would have M=2 and r=2. Let's sub these two sets into the equation:
Earth. F = M/r^2 = 1/1
New planet. F = M/r^2 = 2/4 = 1/2
So you can see that the force on the new planet is half of that felt on Earth.
The question tells us that the force on earth is 500n for this person, so then on the new planet it would be half! So, 250n!