Calculating Horizontal Velocity with Angles

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To calculate the horizontal velocity of a passenger walking up stairs at a 45-degree angle on a boat moving at 1.5 m/s, one must consider the components of the passenger's velocity. The vertical component of the passenger's velocity is 0.5 m/s, which can be resolved into horizontal and vertical components using trigonometric functions. Since the stairs are angled at 45 degrees, both the horizontal and vertical components will be equal, meaning the horizontal velocity from the stairs is 0.5 m/s. The total horizontal velocity of the passenger relative to the water combines the boat's speed and the horizontal component from walking up the stairs, resulting in a final calculation. Understanding how to apply sine and cosine to resolve the triangle formed by the velocities is crucial for finding the correct answer.
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Homework Statement


A passenger on a boat moving at 1.5m/s on a still lake walks up a set of stairs at .5m/s. he stairs are angled at 45 degrees in the direction of motion as shown. What is the velocity of the passenger relative to the water.


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The Attempt at a Solution


How do I find the horizontal velocity of the passenger. Do I take half of the velocity because the angle is 45 degrees? I don't know which equations I should use to find the passengers horizontal velocity.
 
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If you draw a line representing the surface of the water, a line representing the stairs and draw a perpendicular, you will see a right triangle. ".5 m/s" is the rate of change along the hypotenuse of that right triangle. Do you know how to find the lengths of the two legs of a right triangle if you know the length of the hypotenuse and an angle? Using, say, sine and cosine?
 

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