A body of mass 5 kg stJrls from the origin with an initial velocity `bar(u)=(30hati+40hatj)ms^(-1)` .If a constant force `(-6hati-5hatj)N` acts on the body, the time in velocity, which the y-component of the velocity becomes zero is.

Options

A. 5 s
B. 20 s
C. 40 s
D. 80 s

Answer

To solve the problem step by step, we will follow the physics principles of motion under constant acceleration.

### Step 1: Identify the given quantities
- Mass of the body, \( m = 5 \, \text{kg} \)
- Initial velocity, \( \mathbf{u} = 30 \hat{i} + 40 \hat{j} \, \text{m/s} \)
- Force acting on the body, \( \mathbf{F} = -6 \hat{i} - 5 \hat{j} \, \text{N} \)

### Step 2: Calculate the acceleration
Using Newton's second law, the acceleration \( \mathbf{a} \) can be calculated as:
\[ \mathbf{a} = \frac{\mathbf{F}}{m} \]
Substituting the values:
\[ \mathbf{a} = \frac{-6 \hat{i} - 5 \hat{j}}{5} = -1.2 \hat{i} - 1 \hat{j} \, \text{m/s}^2 \]

### Step 3: Write the equation for the y-component of velocity
The y-component of velocity \( v_y \) at time \( t \) can be expressed as:
\[ v_y = u_y + a_y \cdot t \]
Where:
- \( u_y = 40 \, \text{m/s} \) (initial y-component of velocity)
- \( a_y = -1 \, \text{m/s}^2 \) (y-component of acceleration)

### Step 4: Set the y-component of velocity to zero
We need to find the time \( t \) when the y-component of velocity becomes zero:
\[ 0 = 40 - 1 \cdot t \]

### Step 5: Solve for time \( t \)
Rearranging the equation:
\[ t = 40 \, \text{s} \]

### Final Answer
The time in which the y-component of the velocity becomes zero is \( t = 40 \, \text{s} \).

---