# Horizontal Velocity Problem

A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18.0 m/s. The cliff is 50.0 m above a flat, horizontal beach as shown in the figure. (a) What are the coordinates of the initial position of the stone? (b) What are the components of the initial velocity? (c) Write the equations for the x- and y-components of the velocity of the stone with time. (d) Write the equations for the position of the stone with time, using the coordinates in the figure. (e) How long after being released does the stone strike the beach below the cliff? (f) With what speed and angle of impact does the stone land?

To solve this problem, we begin by analyzing the stone's motion in two separate directions: horizontal (x) and vertical (y). Since the stone is thrown horizontally, the initial velocity has no vertical component.

(a) The initial position of the stone is at the edge of the cliff. Since it's 50.0 m above the beach, the coordinates are (0, 50.0) where 0 is the horizontal position and 50.0 is the height above the ground.

(b) The components of the initial velocity are 18.0 m/s horizontally and 0 m/s vertically, since the stone is thrown straight out without an upward or downward angle.

(c) For velocity, the horizontal component remains constant at 18.0 m/s because there's no horizontal acceleration. The vertical velocity increases over time due to gravity, starting at 0 m/s and increasing downward as time passes.

(d) The horizontal position changes steadily with time because of the constant velocity, while the vertical position decreases due to the pull of gravity. The horizontal position increases linearly, and the vertical position decreases quadratically with time.

(e) To find how long it takes for the stone to hit the beach, use the vertical motion, starting with the height of 50.0 m and factoring in gravity. The time is determined by how long it takes for the stone to fall to the ground.

(f) The final speed is found by combining the horizontal and vertical velocities at the moment the stone hits the ground. The angle of impact can be calculated using the ratio of the vertical to horizontal velocities at that time.

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