A player takes 0.1s I catching a ball of mass 150 g moving with velocity of 20 m/s. The force imparted by the ball on the hands of the player is

Options

A. 0.3 N
B. 3 N
C. 30 N
D. 300 N

Answer

To solve the problem of finding the force imparted by the ball on the hands of the player, we can follow these steps:

### Step 1: Convert the mass of the ball from grams to kilograms.
The mass of the ball is given as 150 grams. To convert this to kilograms, we use the conversion factor \(1 \text{ kg} = 1000 \text{ g}\).

\[ m = 150 \text{ g} = \frac{150}{1000} \text{ kg} = 0.15 \text{ kg} \]

### Step 2: Determine the initial velocity of the ball.
The initial velocity of the ball is given as \(20 \text{ m/s}\). When the player catches the ball, the final velocity becomes \(0 \text{ m/s}\) since the ball comes to rest in the player's hands.

### Step 3: Calculate the change in velocity (\(\Delta v\)).
The change in velocity can be calculated as:

\[ \Delta v = v_f - v_i = 0 \text{ m/s} - 20 \text{ m/s} = -20 \text{ m/s} \]

### Step 4: Calculate the acceleration (\(a\)) of the ball.
Using the formula for acceleration, which is the change in velocity divided by the time taken, we have:

\[ a = \frac{\Delta v}{\Delta t} = \frac{-20 \text{ m/s}}{0.1 \text{ s}} = -200 \text{ m/s}^2 \]

### Step 5: Calculate the force (\(F\)) exerted by the ball on the player's hands.
Using Newton's second law, \(F = m \cdot a\):

\[ F = 0.15 \text{ kg} \cdot (-200 \text{ m/s}^2) = -30 \text{ N} \]

The negative sign indicates that the force is in the opposite direction of the ball's initial motion. However, the magnitude of the force is what we are interested in, so we take:

\[ F = 30 \text{ N} \]

### Final Answer:
The force imparted by the ball on the hands of the player is **30 N**.

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