A motor car is going due north at a speed of 50 km/h. It makes a `90^0` left turn without changing the speed. The change in the velocity of the car is about

Options

A. 50 km/h towards west
B. 70 km/h towards south-west
C. 70 km/h towards north-west
D. zero

Answer

To solve the problem, we need to find the change in velocity of a motor car that makes a 90-degree left turn while maintaining its speed. Here’s a step-by-step solution:

### Step 1: Understand the Initial Velocity
The car is initially moving due north with a speed of 50 km/h. We can represent this velocity vector as:
- **Initial Velocity (V_i)** = 50 km/h North.

### Step 2: Determine the Final Velocity
After making a 90-degree left turn, the car will be moving due west, still at a speed of 50 km/h. We can represent this final velocity vector as:
- **Final Velocity (V_f)** = 50 km/h West.

### Step 3: Represent the Velocities as Vectors
We can represent the initial and final velocities as vectors:
- **V_i** = (0, 50) km/h (North direction)
- **V_f** = (-50, 0) km/h (West direction)

### Step 4: Calculate the Change in Velocity
The change in velocity (ΔV) can be calculated using the formula:
\[ \Delta V = V_f - V_i \]
Substituting the vectors:
\[ \Delta V = (-50, 0) - (0, 50) \]
\[ \Delta V = (-50, -50) \]

### Step 5: Find the Magnitude of the Change in Velocity
To find the magnitude of the change in velocity, we can use the Pythagorean theorem:
\[ |\Delta V| = \sqrt{(-50)^2 + (-50)^2} \]
\[ |\Delta V| = \sqrt{2500 + 2500} \]
\[ |\Delta V| = \sqrt{5000} \]
\[ |\Delta V| = 70.71 \text{ km/h} \]

### Step 6: Determine the Direction of the Change in Velocity
The direction of the change in velocity vector (-50, -50) indicates that it is directed towards the southwest.

### Final Answer
The change in the velocity of the car is approximately **70.71 km/h towards the southwest**.

---