Answer:
Step-by-step explanation:
To find the resultant of two velocity vectors, we can use vector addition. Given two velocity vectors v1 and v2, their resultant vector vR can be found by adding the two vectors:
vR = v1 + v2
The angle that the resultant moves with the first vector can be found using trigonometry. If we let theta be the angle between v1 and vR, then we can use the following formula:
tan(theta) = (vR_y / vR_x)
where vR_x is the x-component of the resultant vector and vR_y is the y-component of the resultant vector.
Alternatively, we can use the dot product to find the angle between the two vectors. The dot product of two vectors is defined as:
v1 . v2 = |v1| |v2| cos(theta)
where |v1| and |v2| are the magnitudes of the vectors and theta is the angle between them. Solving for theta, we get:
theta = acos((v1 . v2) / (|v1| |v2|))
where acos is the inverse cosine function.
To summarize:
Find the resultant vector vR by adding the two velocity vectors v1 and v2: vR = v1 + v2
Find the angle theta between v1 and vR using either the tangent formula or the dot product formula:
a. tan(theta) = (vR_y / vR_x)
b. theta = acos((v1 . v2) / (|v1| |v2|))