Question

if 3m/s 4m/s and 12m/s are respectively x y z components of the velocity of an object at any time 't',in the space,the resultant velocity of the object at that time is

Answer 1

Given:

3m/s , 4m/s and 12m/s are respectively x ,y ,z components of the velocity of an object at any time 't' in the space.

To find:

Net velocity?

Calculation:

Since the velocity vectors are expressed in perpendicular vectors, the net velocity is given as:

$\sf v_{net} = \sqrt{ {v_{x}}^{2} + {v_{y}}^{2} + {v_{z}}^{2} }$

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

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

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

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

So, net velocity is 13 m/s.

Answer 2

Explanation:

Given:

3m/s , 4m/s and 12m/s are respectively x ,y ,z components of the velocity of an object at any time 't' in the space.

To find:

Net velocity?

Calculation:

Since the velocity vectors are expressed in perpendicular vectors, the net velocity is given as:

\sf v_{net} = \sqrt{ {v_{x}}^{2} + {v_{y}}^{2} + {v_{z}}^{2} } v

net

=

v

x

2

+v

y

2

+v

z

2

\sf \implies \: v_{net} = \sqrt{ {3}^{2} + {4}^{2} + {12}^{2} } ⟹v

net

=

3

2

+4

2

+12

2

\sf \implies \: v_{net} = \sqrt{ 9 + 16 + 144} ⟹v

net

=

9+16+144

\sf \implies \: v_{net} = \sqrt{ 169} ⟹v

net

=

169

\sf \implies \: v_{net} = 13 \: m {s}^{ - 1} ⟹v

net

=13ms

−1

So, net velocity is 13 m/s.

thanks