Question

2. A body in motion has velocity of 5i +2j-3k and it is acted upon by a constant force of 4i +3j-2k compute the instantaneous power and the angle between the force and velocity

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Answer 1

In order to calculate the instantaneous power, we can use the dot product of the force vector and the velocity vector. The dot product is defined as:

F·V = (4i + 3j - 2k)·(5i + 2j - 3k) = (45) + (32) + (-2*-3) = 20 + 6 - 6 = 20

So the instantaneous power is 20.

To calculate the angle between the force and velocity vectors, we can use the formula:

cos(θ) = (F·V) / (||F|| * ||V||)

where θ is the angle between the vectors, F is the force vector, V is the velocity vector, and ||F|| and ||V|| are the magnitudes of the force and velocity vectors.

First, we need to find the magnitudes:

||F|| = sqrt(4^2 + 3^2 + (-2)^2) = 5

||V|| = sqrt(5^2 + 2^2 + (-3)^2) = sqrt(29)

So we can now calculate the angle:

cos(θ) = (20) / (5 * sqrt(29))

We can get the angle by using the inverse cosine function (arccos)

angle = arccos(cos(θ))

Note that the angle is in radians, if you want to get the angle in degrees, you can use the conversion factor of 180/π.