A car is traveling in a direction 38.0
◦
from +x-axis with a speed of 5.50 m/s relative to the water. A
passenger is walking with a velocity of 2.50 m/s in the +x direction relative to the car. What is the
velocity (magnitude and direction) of the passenger with respect to the water?
To find the velocity of the passenger with respect to the water, we need to consider the velocities of both the car and the passenger relative to the water and then add them.
Let's break down the problem:
1. Start by noting the velocity of the car relative to the water. The car is traveling at a speed of 5.50 m/s in a direction 38.0° from the +x-axis. We'll refer to this as v_car.
2. Next, determine the velocity of the passenger relative to the car. The passenger is walking at a speed of 2.50 m/s in the +x direction relative to the car (since the car is our reference frame). We'll refer to this as v_passenger_rel_to_car.
3. Now, to find the velocity of the passenger with respect to the water (v_passenger_rel_to_water), we have to add the velocities of the car and the passenger relative to the water. We can use vector addition for this.
a) Start by defining the x-axis and y-axis relative to the water.
b) Break down the velocity of the car (v_car) into its x-component and y-component using trigonometry. The x-component can be found by multiplying the magnitude of v_car by the cosine of the angle (38.0°), and the y-component can be found by multiplying the magnitude of v_car by the sine of the angle.
c) Now add the x-components and y-components of v_car and v_passenger_rel_to_car separately to get the x-component and y-component of v_passenger_rel_to_water.
d) Finally, combine the x-component and y-component of v_passenger_rel_to_water using the Pythagorean theorem to find its magnitude, and use trigonometry to find its direction.
By following these steps, you should be able to calculate the velocity (magnitude and direction) of the passenger with respect to the water.