Question

A passenger on a boat moving at 1.90m/s on a still lake walks up a flight of stairs at a speed of 0.60 m/s (Figure 1) . The stairs are angled at 45∘ pointing in the direction of motion as shown. What is the magnitude of the velocity of the passenger relative to the water? What is the direction of the velocity of the passenger relative to the water (counterclockwise from the positive x axis)?

Answer 1

@ash2326 help please :)

Answer 2

It's a simple vector addition problem

Answer 3

velocity of passenger relative to water = velocity of passenger relative to boat + velocity of boat relative to water

Answer 4

So would the velocity of passenger relative to boat be 1.90 m/s?

Answer 5

No, that is the velocity of the boat relative to the water

Answer 6

The velocity of the passenger relative to the boat is the 0.6m/s at an upward angle of 45 degrees (also relative to the boat)

Answer 7

So what would you do with the 45 degrees?

Answer 8

Resolve the .6 m/s at 45 degrees to a horizontal component (same direction as boat)
Add that to the 1.90 m/s of the boat to get your speed relative to the lake

Answer 9

You can add that because the motion up the stairs is in the direction of the motion of the boat.

Answer 10

The question asks for the magnitude of the passenger's velocity relative to the water, not quite what you have suggested radar.
smile123 do you know how to add vectors graphically, top to tail, you should try that first with a sketch

Answer 11

I believe, as I suggested by resolving the 45 degree motion of .m/s which would be Cos45 times .6 or 0.42 m/s to the 1.90 for a total of 2.32 m/s is the results of her movement with respect to the water. I don't know what you would do with vertical component of the stair motion. which is also 0.42 m/s.

Answer 12

I think that is the second part of the question.

Answer 13

what you've calculated is the horizontal component of the velocity with respect to the water.
the question asks for the magnitude of the velocity in a reference frame that is stationary with respect to the water, not the same thing.

Answer 14

magnitude is calculated from the horizontal and vertical components in the usual way

Answer 15

The 2.32 m/s for the first part is correct, but I don't understand how to figure out the second part.

Answer 16

Nevermind I figured it out! Thank you for everyone's help!

Answer 17

This shows the steps used to get the 2nd part.