Concept explainers
The radius
Answer to Problem 11.152P
The radius
Explanation of Solution
Given Information:
The three dimensional motion of a particle is defined by the position
The curve described by the particle lies on the hyperboloid is
The value of A and B are 3 and 1 respectively.
Calculation:
Write the three dimensional motion of a particle position vector equation.
Here, x is
Consider x:
Consider y:
Consider z:
Calculate the
Substitute
Check whether the position vector equation satisfied the curve equation or not.
Substitute
Hence, the equation is satisfied.
Rewrite the Equation (1).
Substitute 3 for A and 1 for B in Equation (1).
Write the expression for velocity using the relation:
Substitute
Calculate velocity vector
Substitute 0 for t in Equation (5).
Here,
Calculate the velocity
Substitute
Write the expression for acceleration vector
Substitute
Substitute 0 sec for t.
Here,
Calculate the magnitude
Substitute 0 is
When time (t) is zero the above equation become zero,
The tangential acceleration
Write the expression for normal component of acceleration
Calculate the radius
Substitute
Substitute 0 for
Substitute
Therefore, the radius
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Chapter 11 Solutions
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