Relative to the ground, a car has a velocity of 14.8 m/s, directed due north. Relative to this car, a truck has a velocity of 24.0 m/s, directed 52.0° north of east. What is the magnitude of the truck's velocity relative to the ground?

V truck = Vtruck rel + V car

Vnorth = 24 sin 52 + 14.8
Veast = 24 cos 52

V^2 = sqrt (Vn^2 + Ve^2)

36.81m/s

To find the magnitude of the truck's velocity relative to the ground, we can use vector addition.

1. Convert the truck's velocity into its components:
- Velocity in the x-direction = 24.0 m/s * cos(52.0°)
- Velocity in the y-direction = 24.0 m/s * sin(52.0°)

2. Add the components of the car's velocity and the truck's velocity in the y-direction:
- Total y-component = 14.8 m/s + Velocity in the y-direction

3. Combine the x-component of the truck's velocity and the car's velocity:
- Combined x-component = Velocity in the x-direction

4. Use the Pythagorean theorem to find the magnitude of the truck's velocity relative to the ground:
- Magnitude of the truck's velocity relative to the ground = √[(Combined x-component)^2 + (Total y-component)^2]

To find the magnitude of the truck's velocity relative to the ground, we can break down the truck's velocity into its north and east components and then use vector addition.

Given:
- Car's velocity relative to the ground = 14.8 m/s due north
- Truck's velocity relative to the car = 24.0 m/s, at an angle of 52.0° north of east

Step 1: Resolve the truck's velocity into its north and east components.
To do this, we use trigonometry. The north component can be found by multiplying the truck's velocity by the sine of the angle, and the east component can be found by multiplying the truck's velocity by the cosine of the angle.

North Component = Velocity of Truck × sin(Angle) = 24.0 m/s × sin(52.0°) = 18.3795 m/s (rounded to 4 decimal places)
East Component = Velocity of Truck × cos(Angle) = 24.0 m/s × cos(52.0°) = 15.2523 m/s (rounded to 4 decimal places)

Step 2: Add the north components and east components separately.
To find the total north component, we add the north component of the truck's velocity to the car's velocity.
Total North Component = Car's Velocity + North Component of Truck's Velocity = 14.8 m/s + 18.3795 m/s = 33.1795 m/s (rounded to 4 decimal places)

To find the total east component, we add the east component of the truck's velocity to zero, as the car's velocity is purely north.
Total East Component = East Component of Truck's Velocity + 0 = 15.2523 m/s (rounded to 4 decimal places)

Step 3: Use the Pythagorean theorem to find the magnitude of the truck's velocity relative to the ground.
The magnitude of the truck's velocity relative to the ground is the square root of the sum of the squares of the north and east components.

Magnitude = √(Total North Component^2 + Total East Component^2) = √(33.1795^2 + 15.2523^2) = √(1099.0323 + 232.7692) = √(1231.8015) = 35.0881 m/s (rounded to 4 decimal places)

Therefore, the magnitude of the truck's velocity relative to the ground is approximately 35.0881 m/s.