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A person looking out the window of a stationary train notices that raindrops are falling vertically down at a speed of 5.0 m/s relative to the ground. When the train moves at a constant velocity, the raindrops make an angle of 25 when they move past the window, as the drawing shows. How fast is the train moving?

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$v_{G T}=2.33 \mathrm{m} \cdot \mathrm{s}^{-1}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Rutgers, The State University of New Jersey

University of Washington

Simon Fraser University

Hope College

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

10:12

A vector is a mathematical entity that has a magnitude (or length) and direction. The vector is represented by a line segment with a definite beginning, direction, and magnitude. Vectors are added by adding their respective components, and multiplied by a scalar (or a number) to scale the vector.

02:05

A person looking out the w…

00:51

01:47

01:24

A train travels due south …

Raindrops make an angle $\…

02:18

Raindrops make an angle wi…

06:37

02:07

During a rainstorm the pat…

01:45

So the question states that someone on a train looks out a window and sees that the rain is falling at five meters per second straight down and this is while the train is stationary and when the train starts moving at a constant velocity, He notices that the rain appears to move at a 25 degree angle, so we know that the rain while the train is stationary, the velocity vector of this, plus the velocity vector of the speed of the train should be equal to the velocity vector of the rain while the train is moving. So we know that this philosophy vector here is five meters per second. So all we have to do is take the tangent of 25 degrees, which is something as the vector of the trained speed was called Team over the adjacent, which is five meters per second, and we find that the train speed is equal to five times the tangent of 25 degrees, which is the same thing as 2.33 meters per second. And that's the answer

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