A ball is thrown upwards, it takes 4 s to reach back to the ground. Find its initial velocity

Options

A. 30 m/s
B. 10 m/s
C. 40 m/s
D. 20 m/s

Answer

To solve the problem of finding the initial velocity of a ball thrown upwards that takes 4 seconds to return to the ground, we can use the equations of motion. Here’s a step-by-step solution:

### Step 1: Understand the scenario
The ball is thrown upwards and returns to the ground after 4 seconds. This means the total time of flight is 4 seconds. The time taken to reach the maximum height is half of the total time, which is 2 seconds.

### Step 2: Identify the known values
- Total time of flight (T) = 4 seconds
- Time to reach maximum height (t) = T/2 = 2 seconds
- Acceleration due to gravity (a) = -10 m/s² (negative because it acts downwards)

### Step 3: Use the equation of motion
We can use the following equation of motion to find the initial velocity (u):
\[ v = u + at \]
At the maximum height, the final velocity (v) is 0 m/s. Therefore, we can substitute the values into the equation:
\[ 0 = u - 10 \times 2 \]

### Step 4: Solve for initial velocity (u)
Rearranging the equation gives:
\[ u = 10 \times 2 \]
\[ u = 20 \text{ m/s} \]

### Conclusion
The initial velocity of the ball when thrown upwards is **20 m/s**.

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