Question

A police officer is driving due north at 25 m/s. What is the resultant velocity of the police car if a wind from the west is blowing at 10 m/s?

a) 25 m/s due north
b) 15 m/s due north
c) 25 m/s at an angle of 53.13 degrees north of east
d) 15 m/s at an angle of 45 degrees north of east

Answer 1

The resultant velocity of the police car is 25 m/s at an angle of 53.13 degrees north of east.

Step-by-step explanation:

The resultant velocity of the police car is option c) 25 m/s at an angle of 53.13 degrees north of east.

To determine the resultant velocity, we need to add the velocities of the police car and the wind vectorially.

The velocity of the police car is 25 m/s due north, which means it has a speed of 25 m/s in the north direction.

The wind velocity is 10 m/s from the west, which means it has a speed of 10 m/s in the west direction.

Using vector addition, we can determine the resultant velocity as follows:

1. Add the velocities of the police car and the wind:
2. Convert the velocities to their x and y components:
3. Add the x and y components of the velocities separately:
4. Use the resulting x and y components to find the magnitude and direction of the resultant velocity:

After performing these calculations, we find that the resultant velocity of the police car is 25 m/s at an angle of 53.13 degrees north of east, as described in option c).