Question

The kinetic energy of a body of mass 4 kg moving with a velocity of (2î − 4ĵ − k̂) m/s is?

• A. \( 84 \, J \)
• B. \( 63 \, J \)
• C. \( 42 \, J \)
• D. \( 21 \, J \)

Hint:

To find the kinetic energy of an object in vector form, first determine the magnitude of the velocity vector using the Pythagorean theorem and then apply the kinetic energy formula \( KE = \frac{1}{2} m v^2 \).

Answer 1

The Correct Option is C

The kinetic energy (\(KE\)) of an object is given by the formula: \[ KE = \frac{1}{2} m v^2 \] 

Step 1: Calculate the magnitude of velocity 
The velocity vector is given as: \[ \vec{v} = (2\hat{i} - 4\hat{j} - \hat{k}) \, ms^{-1} \] The magnitude of velocity is: \[ |\vec{v}| = \sqrt{(2)^2 + (-4)^2 + (-1)^2} \] \[ = \sqrt{4 + 16 + 1} = \sqrt{21} \, ms^{-1} \]

 Step 2: Compute the kinetic energy 
Given that the mass of the object is \( m = 4 \, kg \), we substitute the values: \[ KE = \frac{1}{2} \times 4 \times 21 \] \[ = 2 \times 21 = 42 \, J \] Thus, the kinetic energy of the body is \( 42 \, J \).