Question

34. If 3 ms-1,4 ms-1 and 12 ms-l are respectively x, y
and z-components of the velocity of an object at
any time '', in the space, then resultant velocity
of the object at that time is
(b) 13 ms-1
(c) 20 ms-1
(d) 25 ms -1
(a) 9 ms-1​

Answer 1

Given:

3 m/s , 4 m/s and 12 m/s are respectively x, y and z-components of the velocity of an object at any time in the space.

To find:

Resultant velocity ?

Calculation:

Since the question has provided the magnitude of velocity vectors for all the three mutually perpendicular components, we can say that:

$\therefore \: v_{net} = \sqrt{ {(v_{x})}^{2} + {(v_{y})}^{2} + {(v_{z})}^{2} }$

$\implies \: v_{net} = \sqrt{ {(3)}^{2} + {(4)}^{2} + {(12)}^{2} }$

$\implies \: v_{net} = \sqrt{9 + 16 + 144 }$

$\implies \: v_{net} = \sqrt{169 }$

$\implies \: v_{net} = 13 \: m {s}^{ - 1}$

So, net velocity of the object is 13 m/s.

$\star$ Hope It Helps