A velocity of 10m/s has its y-components 5root2m/s. calculate its components
Answers
Answer:
The answer to the question is 5\sqrt{2}\ m/s5
2
m/s i.e the x-component of the velocity is 5\sqrt{2}\ m/s5
2
m/s
CALCULATION:
The resultant is given as v= 10 m/s
The y-component is given as v_{y}\ =\ 5\sqrt{2}\ m/sv
y
= 5
2
m/s
We are asked to calculate the x-component i.e v_{x}v
x
v_{x}\ and\ v_{y}v
x
and v
y
are mutually perpendicular to each other.
From parallelogram law of vector addition we know that -
R^2=A^2+B^2+2ABcos\thetaR
2
=A
2
+B
2
+2ABcosθ
Here, \thetaθ is the angle between them.
R^2=A^2+B^2R
2
=A
2
+B
2
[∵ \theta=90^0]θ=90
0
]
Putting the above values we get-
v^2=v_{x}^2+v_{y}^2v
2
=v
x
2
+v
y
2
⇒ v_{x}^2=v^2-v_{y}^2v
x
2
=v
2
−v
y
2
=\ 10^2-(5\sqrt{2})^2= 10
2
−(5
2
)
2
=\ 100-50= 100−50
⇒ v_{x}\ =\sqrt{50}\ m/sv
x
=
50
m/s
=5\sqrt{2}\ m/s=5
2
m/s [ans]