A landing airplane makes contact with the runway with a speed of 78.0 m/s and moves towards the south. After 18.5 seconds, the airplane comes to rest. What is the average acceleration of the airplane during the landing ?

Options

A. `2.11 m//s^(2)`, north
B. 4.22 `m//s^(2)` , north
C. `2.11 m//s^(2)` , south
D. `4.22 m//s^(2)`, south

Answer

To solve the problem of finding the average acceleration of the airplane during landing, we can follow these steps:

### Step 1: Identify the given values
- Initial velocity of the airplane, \( v_1 = 78.0 \, \text{m/s} \) (towards the south)
- Final velocity of the airplane, \( v_2 = 0 \, \text{m/s} \) (comes to rest)
- Time taken to come to rest, \( t = 18.5 \, \text{s} \)

### Step 2: Define the direction
Since the airplane is moving towards the south, we can represent the initial velocity as:
- \( v_1 = -78.0 \, \text{m/s} \) (we use negative to indicate the south direction)

### Step 3: Calculate the change in velocity
The change in velocity (\( \Delta v \)) can be calculated as:
\[ \Delta v = v_2 - v_1 \]
Substituting the values:
\[ \Delta v = 0 - (-78.0) = 78.0 \, \text{m/s} \]

### Step 4: Use the formula for average acceleration
The formula for average acceleration (\( a \)) is given by:
\[ a = \frac{\Delta v}{t} \]
Substituting the values we have:
\[ a = \frac{78.0 \, \text{m/s}}{18.5 \, \text{s}} \]

### Step 5: Calculate the average acceleration
Now, we perform the division:
\[ a \approx 4.22 \, \text{m/s}^2 \]

### Step 6: Determine the direction of the acceleration
Since the airplane is decelerating (slowing down), the acceleration is in the opposite direction to the initial velocity. Therefore, if the initial velocity was towards the south, the average acceleration is directed towards the north.

### Final Answer
The average acceleration of the airplane during landing is approximately:
\[ a \approx 4.22 \, \text{m/s}^2 \, \text{(towards the north)} \]

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