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Question

A sandal is dropped from the top of a 15.0-m-high mast on a ship moving at 1.75 m/s due south. Calculate the velocity of the sandal when it hits the deck of the ship: (a) relative to the ship and (b) relative to a stationary observer on shore. (c) Discuss how the answers give a consistent result for the position at which the sandal hits the deck.

a) $-17.1 \textrm{ m/s}$

b) $17.2 \textrm{ m/s, } 84.2^\circ \textrm{ below horizontal to the South}$

c) The position where the sandal hits the deck of the ship depends on how the x-component of the velocity of the sandal compares with the x-component of the velocity of the ship. From the perspective of a person on the ship, neither the sandal nor the ship have any velocity in the x-direction, and from their perspective the sandal lands straight down from where it started. From the perspective of someone on the shore, the sandal and the ship have the exact same x-component of each of their respective velocities. They each travel the same distance horizontally after the sandal is dropped, and so the sandal lands on the deck at the position directly below where it started -- the same answer in other words compared with the observer on the ship.

Solution Video

# OpenStax College Physics Solution, Chapter 3, Problem 61 (Problems & Exercises) (5:47)

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Submitted by fmiren on Fri, 07/24/2020 - 12:08

Shouldn't the both velocities be negative?

Submitted by ShaunDychko on Fri, 07/24/2020 - 14:57

Hello fmiren,
Thank you very much for your comment. I agree that part (a) should be negative since I implied that down is the negative direction when stating that acceleration due to gravity is negative. I have updated the solution. Part (b), however, I've left unchanged. The purpose of the negative sign is to indicate direction, but the direction is given explicitly, and it doesn't go along one of the axes.
Thanks again, and all the best,
Shaun