While a car is stopped at a traffic light in a storm, rain drops strike the roof of the car. The area of the roof is 5.0 `m^2`. Each raindrop has a mass of `3.7 xx 10^(-4)` kg and speed of 2.5 m/s before impact and is at rest after the impact. If on average at a given time, 150 raindrops strike each square meter, what is the impulse of the rain striking the car ?

Options

A. 0.69 N.s
B. 0.046 N.s
C. 0.14 N.s
D. 11 N.s

Answer

To solve the problem of calculating the impulse of the rain striking the car, we will follow these steps:

### Step 1: Determine the total number of raindrops striking the car
The area of the roof of the car is given as \(5.0 \, m^2\). The average number of raindrops striking each square meter is \(150\). Therefore, the total number of raindrops striking the roof can be calculated as:

\[ \text{Total raindrops} = \text{Area} \times \text{Raindrops per square meter} = 5.0 \, m^2 \times 150 \, \text{raindrops/m}^2 = 750 \, \text{raindrops} \]

### Step 2: Calculate the total mass of the raindrops
Each raindrop has a mass of \(3.7 \times 10^{-4} \, kg\). To find the total mass of all raindrops striking the car, we multiply the total number of raindrops by the mass of one raindrop:

\[ \text{Total mass} = \text{Total raindrops} \times \text{Mass of one raindrop} = 750 \, \text{raindrops} \times 3.7 \times 10^{-4} \, kg = 0.2775 \, kg \]

### Step 3: Calculate the change in momentum
Before impact, the raindrops are moving at a speed of \(2.5 \, m/s\) and come to rest after striking the car. The change in velocity (\(\Delta v\)) is given by:

\[ \Delta v = v_f - v_i = 0 - 2.5 \, m/s = -2.5 \, m/s \]

The change in momentum (\(\Delta p\)) can be calculated using the formula:

\[ \Delta p = \text{Total mass} \times \Delta v \]

Substituting the values we found:

\[ \Delta p = 0.2775 \, kg \times (-2.5 \, m/s) = -0.69375 \, kg \cdot m/s \]

### Step 4: Calculate the impulse
The impulse (\(J\)) experienced by the car due to the rain is equal to the change in momentum:

\[ J = \Delta p = -0.69375 \, kg \cdot m/s \]

Since impulse is often expressed in terms of magnitude, we take the absolute value:

\[ J = 0.69375 \, Ns \]

### Final Result
Thus, the impulse of the rain striking the car is approximately:

\[ J \approx 0.69 \, Ns \]