A stone of 200g is thrown vertically upward at a velocity of 60m/s. The kientic energy of the stone after 7s will be `(g= 10m//s^(2))`

Options

A. 5J
B. 10J
C. 15J
D. 20J

Explanation

To solve the problem, we need to find the kinetic energy of a stone thrown vertically upward after 7 seconds. Here’s a step-by-step breakdown of the solution:

### Step 1: Convert Mass to Kilograms
The mass of the stone is given as 200 grams. We need to convert this to kilograms because the standard unit of mass in physics is kilograms.

\[ m = 200 \text{ g} = \frac{200}{1000} \text{ kg} = 0.2 \text{ kg} \]

**Hint:** Remember to convert grams to kilograms by dividing by 1000.

### Step 2: Determine the Initial Velocity
The initial velocity \( u \) of the stone is given as 60 m/s.

\[ u = 60 \text{ m/s} \]

**Hint:** The initial velocity is the speed at which the stone is thrown upward.

### Step 3: Calculate the Time of Flight
The time of flight for an object thrown vertically upward can be calculated using the formula:

\[ T = \frac{2u}{g} \]

Where \( g \) is the acceleration due to gravity (10 m/s²).

\[ T = \frac{2 \times 60}{10} = 12 \text{ seconds} \]

**Hint:** The total time of flight is the time taken to go up and come back down.

### Step 4: Determine the Time to Reach Maximum Height
The time to reach maximum height is half of the total time of flight.

\[ T_{up} = \frac{T}{2} = \frac{12}{2} = 6 \text{ seconds} \]

**Hint:** The stone takes equal time to go up and come down.

### Step 5: Calculate the Velocity After 7 Seconds
After reaching the maximum height at 6 seconds, the stone will start to fall. We can use the equation of motion to find the velocity after 7 seconds:

\[ v = u - g \cdot t \]

At 7 seconds, the time \( t \) since it started falling is \( 7 - 6 = 1 \) second.

\[ v = 0 + 10 \cdot 1 = 10 \text{ m/s} \]

**Hint:** When the stone reaches its maximum height, its velocity is 0, and then it starts accelerating downward due to gravity.

### Step 6: Calculate the Kinetic Energy
The kinetic energy \( KE \) can be calculated using the formula:

\[ KE = \frac{1}{2} m v^2 \]

Substituting the values we have:

\[ KE = \frac{1}{2} \cdot 0.2 \cdot (10)^2 \]
\[ KE = \frac{1}{2} \cdot 0.2 \cdot 100 = 0.1 \cdot 100 = 10 \text{ joules} \]

**Hint:** Kinetic energy depends on the mass and the square of the velocity.

### Final Answer
The kinetic energy of the stone after 7 seconds is **10 joules**.