Final answer:
The truck's speed relative to the ground is the sum of its relative speed to the police car and the police car's speed. Since the police officer is moving north and the truck is moving east, their speeds in each direction can be added directly, resulting in a ground speed for the truck of 45 m/s.
Step-by-step explanation:
To find the truck's speed relative to the ground, we need to use the concept of relative velocity. The police officer is driving north at 30 m/s while the truck's speed relative to the police car is 15 m/s to the east. This means the truck is moving east faster than the police officer is moving north.
To find the actual speed of the truck relative to the ground, you can set up the problem using vector addition, with the officer's speed being a vector pointing north and the truck's speed relative to the officer being a vector pointing east. The truck's ground speed vector will be the vector sum of these two vectors.
The officer's northward speed does not affect the eastward speed of the truck, so the truck's speed relative to the ground to the east is simply the sum of its relative speed to the officer's car and the officer's speed. Therefore, the truck's speed relative to the ground is 30 m/s + 15 m/s = 45 m/s.