A sandal is dropped from the top of a 15.0 -m-high mast on a...

A sandal is dropped from the top of a 15.0 -m-high mast on a ship moving at $1.75 \mathrm{~m} / \mathrm{s}$ 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.

Key Concepts

Projectile Motion

Projectile motion describes the two-dimensional motion of an object moving under the influence of gravity alone. In these cases, the horizontal and vertical motions are independent; the horizontal component remains constant (ignoring air resistance) while the vertical component is uniformly accelerated due to gravity. This concept is fundamental for solving problems where objects are dropped, thrown, or launched and follow a curved trajectory.

Relative Motion

Relative motion is the study of how the observed motion of an object can differ depending on the observer's frame of reference. It involves transforming the velocity and position from one reference frame (such as a moving vehicle) to another (such as a stationary observer). This concept is crucial when analyzing the motion of an object as seen from either a moving platform or a fixed point.

Vector Addition in Kinematics

Vector addition in kinematics involves combining individual displacement or velocity vectors according to their magnitudes and directions to determine the resultant vector. This process is essential in problems where motion occurs in multiple dimensions, allowing for the accurate calculation of overall velocity, speed, and direction by considering both horizontal and vertical components.

Reference Frames and Galilean Transformation

Reference frames, along with the application of Galilean transformations, allow the translation of physical quantities like velocity and acceleration between different inertial frames. This concept ensures that the laws of motion hold true in all inertial frames and provides a systematic method for converting measurements from one perspective to another, which is particularly useful for linking observations made in a moving frame to those made by a stationary observer.

Transcript

00:01 For part a, we can say vy final squared equals vy initial squared plus 2g times delta y.

00:09 In this case, this is going to be zero, the initial y velocity, and we can say vy final is equaling the square root of 2 times 9 .8 meters per second squared times 15 .0 meters.

00:23 And this is equaling 17 .15 meters per second.

00:30 This would be the velocity relative to the ship because the sandal is actually on the ship.

00:41 Now relative to someone on like a rather an observer that is not on the ship but stationary on shore, we can say that for part b, that we can say that the velocity of the sandal relative to the observer would be equaling the velocity of the sandal relative to the ship plus the velocity of the ship relative to the observer.

01:06 That might the velocity of the sandal relative to the observer equals the velocity of the sandal relative to the ship plus the velocity of the ship relative to the observer.

01:28 That makes more sense.

01:30 And we can say that then we can say that then the magnitude of the velocity of the sandal relative to the observer is going to be equalling the square root of 17 .15 meters per second squared.

01:52 This would be of course the the velocity of the sandal relative to the ship plus the velocity of the ship relative to the observer 1 .75 meters per second quantity squared.

02:05 This is equalling approximately 17 .2 meters per second.

02:12 So this would be the magnitude of the velocity of the sandal relative to the observer on shore...

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