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

Explanation

To solve the problem step by step, we will focus on the y-component of the motion since the question specifically asks for the time when the y-component of the velocity becomes zero.

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

### Step 2: Extract the y-component of the initial velocity and force
- Initial y-component of velocity, \( u_y = 40 \, \text{m/s} \)
- y-component of the force, \( F_y = -5 \, \text{N} \)

### Step 3: Calculate the acceleration using Newton's second law
Using the formula \( \vec{F} = m \vec{a} \):
\[ F_y = m a_y \]
Substituting the known values:
\[ -5 = 5 a_y \]
Solving for \( a_y \):
\[ a_y = \frac{-5}{5} = -1 \, \text{m/s}^2 \]

### Step 4: Use the first equation of motion to find the time when the y-component of velocity becomes zero
The first equation of motion is:
\[ v_y = u_y + a_y t \]
We want to find the time \( t \) when the final y-component of velocity \( v_y = 0 \):
\[ 0 = 40 + (-1) t \]
Rearranging the equation:
\[ t = 40 \, \text{s} \]

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

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