A cruise ship moves southward in still water at a speed of 20.0 km/h, while a passenger on the deck of the ship walks toward the east at a speed of 5.0 km/h .The passengers velocity with respect to Earth is?

√(20^2+5^2)

at an angle θ east from south such that tanθ = 5/20

Ah, my dear friend, let me tell you this delightful tale. Imagine you're on that cruise ship, jauntily strolling towards the east at a speed of 5.0 km/h. Meanwhile, the ship itself is gracefully moving southward at 20.0 km/h.

Now, let's put our thinking hats on. To find the passenger's velocity with respect to Earth, we need to know the combined effect of their individual velocities. We can simply use the Pythagorean theorem to find the resultant velocity.

So, here we go: the square of the passenger's eastward velocity (5.0 km/h) plus the square of the cruise ship's southward velocity (20.0 km/h) equals the square of the resultant velocity. Ah, math, you always find a way to sneak in!

Calculating this captivating equation, we get √(5.0^2 + 20.0^2) km/h ≈ 20.4 km/h. Voilà! The passenger's velocity with respect to Earth is approximately 20.4 km/h, combining their eastward walk and the ship's southward movement.

Remember, my friend, to always appreciate the wonders of physics and the ridiculousness of cruise ship pedestrians. Bon voyage!

To find the passenger's velocity with respect to Earth, we need to consider both the ship's velocity and the passenger's velocity.

The ship's velocity, moving southward in still water at a speed of 20.0 km/h, can be represented as 20.0 km/h south.

The passenger's velocity, walking toward the east at a speed of 5.0 km/h, can be represented as 5.0 km/h east.

To find the resultant velocity, we can use vector addition. Since the two velocities are at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the resultant velocity:

Resultant velocity^2 = (ship's velocity)^2 + (passenger's velocity)^2

Resultant velocity^2 = (20.0^2 km/h^2) + (5.0^2 km/h^2)
Resultant velocity^2 = 400.0 km^2/h^2 + 25.0 km^2/h^2
Resultant velocity^2 = 425.0 km^2/h^2

Taking the square root of both sides:

Resultant velocity ≈ √(425.0) ≈ 20.62 km/h

So, the passenger's velocity with respect to Earth is approximately 20.62 km/h.

To find the passenger's velocity with respect to Earth, we need to consider both the ship's velocity and the passenger's velocity. Since the passenger is walking on the deck of the moving ship, their velocity is relative to the ship's velocity.

Given:
- The ship's velocity is 20.0 km/h southward.
- The passenger's velocity is 5.0 km/h eastward relative to the ship.

To find the passenger's velocity with respect to Earth, we need to combine these two velocities using vector addition. We'll use the Pythagorean theorem because the velocities are at right angles to each other.

1. Square the ship's velocity component in the southward direction: (20.0 km/h)² = 400.0 km²/h².
2. Square the passenger's velocity component in the eastward direction: (5.0 km/h)² = 25.0 km²/h².
3. Add the squared components: 400.0 km²/h² + 25.0 km²/h² = 425.0 km²/h².
4. Take the square root to find the magnitude of the resultant velocity: √(425.0 km²/h²) ≈ 20.61 km/h.

The direction of the velocity can be found using trigonometry. Since the passenger is walking eastward, which is perpendicular to the ship's southward direction, we have a right-angled triangle. The tangent of the angle between the resultant velocity and the eastward direction is given by:

tan(θ) = (20.0 km/h) / (5.0 km/h) = 4.

Taking the inverse tangent of both sides, θ ≈ 76.87°.

Therefore, the passenger's velocity with respect to Earth is approximately 20.61 km/h at an angle of 76.87° east of south.