A packet is dropped from a balloon which is going upwards with the velocity `12m//s`. The velocity of the packet after 2 seconds will be

Options

A. `-12 m//s`
B. `12m//s`
C. `-7.6 m//s`
D. `7.6 m//s`

Answer

To solve the problem of finding the velocity of a packet dropped from a balloon moving upwards with an initial velocity of 12 m/s after 2 seconds, we can follow these steps:

### Step 1: Identify the initial conditions
- The initial velocity of the packet (u) when it is released from the balloon is 12 m/s (upward).
- The acceleration due to gravity (g) acts downward and has a value of approximately 9.8 m/s².

### Step 2: Determine the direction of the forces
- Since the packet is moving upward initially and gravity acts downward, we will consider the upward direction as positive and the downward direction as negative.

### Step 3: Use the kinematic equation
We can use the following kinematic equation to find the final velocity (v) of the packet after a time (t):
\[ v = u - gt \]
Here,
- \( u = 12 \, \text{m/s} \) (upward),
- \( g = 9.8 \, \text{m/s}^2 \) (downward),
- \( t = 2 \, \text{s} \).

### Step 4: Substitute the values into the equation
Substituting the known values into the equation:
\[ v = 12 \, \text{m/s} - (9.8 \, \text{m/s}^2 \times 2 \, \text{s}) \]

### Step 5: Calculate the acceleration term
Calculate \( 9.8 \, \text{m/s}^2 \times 2 \, \text{s} \):
\[ 9.8 \times 2 = 19.6 \, \text{m/s} \]

### Step 6: Complete the calculation for final velocity
Now, substitute this back into the equation:
\[ v = 12 \, \text{m/s} - 19.6 \, \text{m/s} \]
\[ v = 12 - 19.6 = -7.6 \, \text{m/s} \]

### Step 7: Interpret the result
The negative sign indicates that after 2 seconds, the packet is moving downward with a velocity of 7.6 m/s.

### Final Answer
The velocity of the packet after 2 seconds will be **-7.6 m/s** (downward).

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