Work in general is given by W=F·d where F is the force vector and d is the displacement vector. The dot symbol is the dot product which is a measure of how parallel two vectors are. It can be replaced by the cosine of the angle between the two vectors and the vectors replaced by their magnitudes. If F and d are parallel then the angle is zero and the cosine is unity. So in this case work can be defined as the product of the magnitudes of the force and distance:
W=Fd
The addition of vectors involve both magnitude and direction. In this case, we make use of a triangle to visualize the problem. The length of two sides were given while the measure of the angle between the two sides can be derived. We then assign variables for each of the given quantities.
Let:
b = length of one side = 8 m
c = length of one side = 6 m
A = angle between b and c = 90°-25° = 75°
We then use the cosine law to find the length of the unknown side. The cosine law results to the formula: a^2 = b^2 + c^2 -2*b*c*cos(A). Substituting the values, we then have: a = sqrt[(8)^2 + (6)^2 -2(8)(6)cos(75°)]. Finally, we have a = 8.6691 m.
Next, we make use of the sine law to get the angle, B, which is opposite to the side B. The sine law results to the formula: sin(A)/a = sin(B)/b and consequently, sin(75)/8.6691 = sin(B)/8. We then get B = 63.0464°. However, the direction of the resultant vector is given by the angle Θ which is Θ = 90° - 63.0464° = 26.9536°.
In summary, the resultant vector has a magnitude of 8.6691 m and it makes an angle equal to 26.9536° with the x-axis.
Answer:
The ratio is 9.95
Solution:
As per the question:
Amplitude, 
Wavelength, 
Now,
To calculate the ratio of the maximum particle speed to the speed of the wave:
For the maximum speed of the particle:
where
= angular speed of the particle
Thus
Now,
The wave speed is given by:
Now,
The ratio is given by:
Answer:
Hope it helps for you :)))))
Answer:The sled slides 16.875m before rest.
Explanation:
a=0.6 m/s²
