A professional diver of mass `60kg` performs a dive from a platform `10m` above the water surface. Find the magnitude of the average impact force experienced by him if the impact time is `1s` on collision with water surface. Assume that the velocity of the diver just after enering the water surface is `4ms^(-1)(g =10 ms^(-2))` .

Options

A. `240N`
B. `600N`
C. `300N`
D. `60N`

Explanation

To solve the problem of finding the magnitude of the average impact force experienced by the diver, we can follow these steps:

### Step 1: Calculate the final velocity of the diver just before hitting the water.
We can use the equation of motion for this:
\[ V = U + gt \]
Where:
- \( V \) = final velocity just before hitting the water
- \( U \) = initial velocity (which is 0 m/s since the diver starts from rest)
- \( g \) = acceleration due to gravity (10 m/s²)
- \( t \) = time of fall (which we need to calculate)

First, we need to calculate the time taken to fall 10 m using the equation:
\[ h = \frac{1}{2}gt^2 \]
Rearranging gives:
\[ t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 10}{10}} = \sqrt{2} \approx 1.41 \text{ seconds} \]

Now, substituting into the velocity equation:
\[ V = 0 + 10 \times 1.41 \approx 14.1 \text{ m/s} \]

### Step 2: Calculate the change in velocity (ΔV).
The change in velocity is given by:
\[ \Delta V = V - U \]
Where:
- \( V \) = final velocity just before hitting the water (14.1 m/s)
- \( U \) = initial velocity just before entering the water (4 m/s)

Thus,
\[ \Delta V = 14.1 - 4 = 10.1 \text{ m/s} \]

### Step 3: Calculate the average impact force (F).
Using the formula for average impact force:
\[ F = \frac{m \cdot \Delta V}{t} \]
Where:
- \( m \) = mass of the diver (60 kg)
- \( \Delta V \) = change in velocity (10.1 m/s)
- \( t \) = impact time (1 s)

Substituting the values:
\[ F = \frac{60 \cdot 10.1}{1} = 606 \text{ N} \]

### Step 4: Round off the result.
Since the problem may require rounding, we can round 606 N to 600 N for simplicity.

### Final Answer:
The magnitude of the average impact force experienced by the diver is approximately **600 N**.

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