A body is thrown vertically upwards and rises to a height of 10m. The velocity with which the body was thrown is (g - 9.8m/(`s^(2)`)

Options

A. 10m/s
B. 20m/s
C. 14m/s
D. none of these

Answer

To solve the problem of finding the initial velocity with which a body is thrown vertically upwards to reach a height of 10 meters, we can use the equations of motion. Here’s a step-by-step solution:

### Step 1: Understand the problem
We know that the body reaches a maximum height (h) of 10 meters. At this height, the final velocity (v) of the body is 0 m/s (since it momentarily stops before falling back down). The acceleration due to gravity (g) is acting downwards and is given as 9.8 m/s².

### Step 2: Use the equation of motion
We can use the second equation of motion:
\[ v^2 = u^2 + 2as \]
where:
- \( v \) = final velocity (0 m/s at the maximum height)
- \( u \) = initial velocity (what we need to find)
- \( a \) = acceleration (which is -g, or -9.8 m/s² since it acts downward)
- \( s \) = displacement (which is the height, 10 m)

### Step 3: Substitute the known values
Substituting the known values into the equation:
\[ 0 = u^2 + 2(-9.8)(10) \]

### Step 4: Simplify the equation
This simplifies to:
\[ 0 = u^2 - 196 \]
Rearranging gives:
\[ u^2 = 196 \]

### Step 5: Solve for initial velocity
Taking the square root of both sides:
\[ u = \sqrt{196} \]
Calculating this gives:
\[ u = 14 \, \text{m/s} \]

### Conclusion
Thus, the initial velocity with which the body was thrown is **14 m/s**.

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