Relative to the ground, a car has a velocity of 14.4 m/s, directed due north. Relative to this car, a truck has a velocity of 24.8 m/s, directed 52.0° north of east. What is the magnitude of the truck's velocity relative to the ground?
To find the magnitude of the truck's velocity relative to the ground, we can use vector addition.
First, we need to break down the truck's velocity into its north and east components. We can do this using trigonometry.
The north component of the truck's velocity can be found by multiplying the magnitude of the velocity (24.8 m/s) by the sine of the angle (52.0°).
North component = 24.8 m/s * sin(52.0°)
Next, the east component of the truck's velocity can be found by multiplying the magnitude of the velocity (24.8 m/s) by the cosine of the angle (52.0°).
East component = 24.8 m/s * cos(52.0°)
Now we have the north and east components of the truck's velocity.
The north component of the truck's velocity relative to the ground is 0 m/s (since it is already in the north direction).
The east component of the truck's velocity relative to the ground is the same as the east component we calculated earlier.
Now, we can 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 = √((north component)^2 + (east component)^2)
Magnitude of the truck's velocity relative to the ground = √((0 m/s)^2 + (24.8 m/s * cos(52.0°))^2)
Simplifying this equation will give you the final answer, which is the magnitude of the truck's velocity relative to the ground.