a pet truck is moving at 25m/s north, a dog inside moves at 1.75 m/s at angle 35 degrees east of north. What is the velocity of the dog relative to the road?

Rat🐀🐀 race is my favorite Dog

Well, I guess you could say the dog is just trucking along! Oh wait, that's a good one. So, let's break it down.

The truck is moving at 25 m/s north, while the dog is moving at 1.75 m/s at an angle 35 degrees east of north.

To find the velocity of the dog relative to the road, we can use some basic vector math. We need to split the dog's velocity into north and east components.

The north component of the dog's velocity is 1.75 m/s * cos(35°) = 1.43 m/s.

The east component of the dog's velocity is 1.75 m/s * sin(35°) = 1.00 m/s.

Now we can add the north component of the dog's velocity to the truck's velocity: 25 m/s + 1.43 m/s = 26.43 m/s north.

And we add the east component of the dog's velocity to the truck's east velocity (which is 0 m/s): 0 m/s + 1.00 m/s = 1.00 m/s east.

So, the velocity of the dog relative to the road is 26.43 m/s north and 1.00 m/s east. I guess you could say the dog is going in the right direction!

To find the velocity of the dog relative to the road, we need to use vector addition. The velocity of the truck is given as 25 m/s north, and the velocity of the dog is given as 1.75 m/s at an angle 35 degrees east of north.

First, we need to break down the velocity of the dog into its north and east components. The north component can be found by multiplying the magnitude of the velocity (1.75 m/s) by the cosine of the angle (cos(35°)):

North component of the dog's velocity = 1.75 m/s * cos(35°)

Next, we need to find the east component of the dog's velocity. This can be found by multiplying the magnitude of the velocity (1.75 m/s) by the sine of the angle (sin(35°)):

East component of the dog's velocity = 1.75 m/s * sin(35°)

Now, we can add the north component of the dog's velocity to the north component of the truck's velocity to get the net northward velocity:

Net northward velocity = 25 m/s + (1.75 m/s * cos(35°))

Finally, we can add the east component of the dog's velocity to the east component of the truck's velocity to get the net eastward velocity:

Net eastward velocity = 0 m/s + (1.75 m/s * sin(35°))

The velocity of the dog relative to the road is then the vector formed by the net northward velocity and the net eastward velocity.

let s be the speed of the dog

s^2 = 25^2 + 1.75^2 - 2(25)(1.75)cos 145°
s = 26.45m/s

Let θ be the direction of travel

sinθ/1.75 = sin145°/26.45
θ = 2.17°

So, the dog's velocity is 26.45 m/s at N2.17°E

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