Question

if v=(3+4j+5k)m/s is the instantaneous velocity of a body of mass 1.5kg .Calculate its kinetic energy.

Answer 1

Correct Question:

If v=(3 i+4 j+5 k)m/s is the instantaneous velocity of a body of mass 1.5kg .Calculate its kinetic energy.

Answer:

• Kinetic Energy (K.E) = 37.5 Joules.

Given:

1. Velocity of the body (v) = 3 i+4 j +5 k m/s.
2. Mass of the Body (M) = 1.5 Kg.

Explanation:

$\rule{300}{1.5}$

We Need to Find the Magnitude of velocity.

v=(3 i+4 j+5 k)m/s

We Know,

$\large{\boxed{\bold{v = \sqrt{(a_x)^2 + (a_y)^2 + (a_z)^2}}}}$

$\bold{Here}\begin{cases}\tt{a_x} \: \text{Denotes x - Component} \\ \tt{a_y} \: \text{Denotes y - Component} \\ \tt{a_z} \: \text{Denotes z - Component}\end{cases}$

Now,

$\large{\boxed{\bold{v = \sqrt{(a_x)^2 + (a_y)^2 + (a_z)^2}}}}$

Substituting the values,

$\large{\tt \hookrightarrow v = \sqrt{(3)^2 + (4)^2 + (5)^2}}$

$\large{\tt \hookrightarrow v = \sqrt{9 + 16 + 25}}$

$\large{\tt \hookrightarrow v = \sqrt{25 + 25}}$

$\large{\tt \hookrightarrow v = \sqrt{25(1 + 1)}}$

$\large{\tt \hookrightarrow v = \sqrt{25 \times 2}}$

$\large{\hookrightarrow{\underline{\underline{\tt v = 5 \sqrt{2} \: m/s}}}}$

$\rule{300}{1.5}$

$\rule{300}{1.5}$

From Kinetic energy Formula,

$\large{\boxed{\bold{K.E = \dfrac{1}{2}Mv^2}}}$

Substituting the values,

$\large{\tt \hookrightarrow K.E = \dfrac{1}{2} \times 1.5 \times (5 \sqrt{2})^2}$

$\large{\tt \hookrightarrow K.E = \dfrac{1}{2} \times 1.5 \times 50}$

$\large{\tt \hookrightarrow K.E = \dfrac{1}{\cancel{2}} \times 1.5 \times \cancel{50}}$

$\large{\tt \hookrightarrow K.E = 1 \times 1.5 \times 25}$

$\large{\tt \hookrightarrow K.E = 1 \times 37.5 }$

$\huge{\boxed{\boxed{\tt K.E = 37.5 \: J}}}$

∴ Kinetic Energy of the body is 37.5 Joules.

$\rule{300}{1.5}$

Answer 2

Correct Question:

➜ If v = (3i + 4j + 5k) m/s is the instantaneous velocity of a body of mass 1.5kg.Calculate its kinetic energy.

Solution:

Given:

➜ If v = (3i + 4j + 5k) m/s is the instantaneous velocity of a body of mass 1.5kg.

Find:

➜ Calculate its kinetic energy.

Formula:

➜ V = √(ax)² + (ay)² + (az)²

Adding the values:

➜ V = √(3)² + (4)² + (5)²

➜ V = √9 + 16 + 25

➜ V = 25 + 25

➜ V = 25 (1 + 1)

➜ V = √25 × 2

➜ V = 5 √2 m/s

Kinetic energy formula:

➜ K.E = 1/2 MV²

Adding values:

➜ K.E = 1/2 × 1.5 × (5 √2)²

➜ K.E = 1/2 × 1.5 × 50

➜ K.E = 1 × 1.5 × 25

➜ K.E = 1 × 37.5

➜ K.E = 37.5 J

Therefore, 37.5 Joules is the kinetic energy of the body.

#AnswerWithQuality

#BAL