A pet-store supply truck moves at 25.0 m/ north along a highway. Inside, a dog moves at 1.75 m/s at an angle of 35.0 degrees east of north. What is the velocity of the dog relative to the road?

Add the two vectors.

sin 35 degrees = 0.57

0.57 *1.75 = 1
25 + 1 = 26

To find the velocity of the dog relative to the road, we need to consider the vector addition of the truck's velocity and the dog's velocity.

The velocity of the truck is given as 25.0 m/s north. Since the truck is moving in a straight line north, its velocity is only in the north direction.

The velocity of the dog is given as 1.75 m/s at an angle of 35.0 degrees east of north. We can break down this velocity into its north and east components using trigonometry.

The north component of the dog's velocity is given by v_dog_north = v_dog * cos(angle), where v_dog is the dog's velocity (1.75 m/s) and angle is the angle east of north (35.0 degrees). Substituting the values, we have:

v_dog_north = 1.75 * cos(35.0)

Similarly, the east component of the dog's velocity is given by v_dog_east = v_dog * sin(angle):

v_dog_east = 1.75 * sin(35.0)

Now, we can find the velocity of the dog relative to the road by adding the north component of the dog's velocity (v_dog_north) to the velocity of the truck (25.0 m/s north):

velocity_relative = v_dog_north + truck_velocity

Substituting the values:

velocity_relative = 1.75 * cos(35.0) + 25.0

Now we just need to calculate the value of velocity_relative to get the final answer.

25.1