Boat Passenger Velocity on Stairs in 2D Motion Problem

[Enjoi_skater06]

Homework Statement

A passenger on a boat moving at 1.25 m/s on a still lake walks up a flight of stairs at a speed of 0.50 m/s, Fig. 3-44. The stairs are angled at 45° pointing in the direction of motion as shown. What is the velocity of the passenger relative to the water?

Magnitude = ___m/s
Direction= ___° (above the water)

Could someone please help me with this problem... I've been stuck on it all night, and can't seem to figure out the correct method of solving it... Help would be greatly appreciated... Thanks =)

 

[learningphysics]

Not sure without the picture. But it seems like a vector addition problem. The velocity of the passenger wrt water, is the vector sum of:

the velocity of the boat wrt water + the velocity of the passenger wrt the boat.

 

[m2003]

I would approach this problem by first breaking it down into its components. We have a boat moving at 1.25 m/s on a still lake, and a passenger walking up a flight of stairs at 0.50 m/s. The stairs are angled at 45° in the direction of motion.

To determine the velocity of the passenger relative to the water, we need to consider the boat's velocity and the passenger's velocity separately. The boat's velocity is constant and is in the direction of motion, so we can represent it as a vector with a magnitude of 1.25 m/s and a direction of 0° (parallel to the water).

The passenger's velocity, on the other hand, is a combination of their walking velocity and the boat's velocity. Since the stairs are angled at 45°, we can use trigonometry to determine the horizontal and vertical components of the passenger's velocity. The horizontal component will be equal to the boat's velocity (1.25 m/s) since it is parallel to the water. The vertical component can be determined using the sine function: sin(45°) = opposite/hypotenuse. Therefore, the vertical component of the passenger's velocity is 0.50 m/s.

To find the overall velocity of the passenger relative to the water, we can use the Pythagorean theorem: v^2 = (1.25 m/s)^2 + (0.50 m/s)^2. This gives us a magnitude of 1.35 m/s.

To determine the direction, we can use the inverse tangent function: tan^-1(0.50/1.25) = 21.8°. This means that the passenger's velocity is 1.35 m/s at an angle of 21.8° above the water's surface.

Therefore, the velocity of the passenger relative to the water is 1.35 m/s at an angle of 21.8° above the water's surface. I hope this explanation helps you understand the problem better. Let me know if you have any further questions.

 

[ogb p]

I would approach this problem by first understanding the concept of relative velocity. In this case, we are looking for the velocity of the passenger relative to the water, which means we need to take into account the velocity of the boat as well.

To solve this problem, we can use the vector addition method. We can break down the velocity of the passenger into horizontal and vertical components, using the given angle of 45°. The horizontal component of the passenger's velocity would be 0.50 m/s cos 45° = 0.354 m/s, and the vertical component would be 0.50 m/s sin 45° = 0.354 m/s.

Next, we can add this horizontal component to the velocity of the boat, which is 1.25 m/s. This gives us a total horizontal velocity of 1.25 m/s + 0.354 m/s = 1.604 m/s.

For the vertical component, since the stairs are angled in the direction of motion, we can assume that the passenger's vertical velocity relative to the water would be the same as the boat's vertical velocity, which is 0 m/s.

Using the Pythagorean theorem, we can find the magnitude of the passenger's velocity relative to the water, which is the hypotenuse of the right triangle formed by the horizontal and vertical components. This gives us a magnitude of √(1.604^2 + 0^2) = 1.604 m/s.

To find the direction of the passenger's velocity relative to the water, we can use trigonometry to find the angle above the water. This would be the inverse tangent of the vertical component (0.354 m/s) divided by the horizontal component (1.604 m/s), which gives us an angle of 13.2° above the water.

Therefore, the velocity of the passenger relative to the water is 1.604 m/s at an angle of 13.2° above the water. I hope this explanation helps you understand the problem better and solve it correctly.