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A student throws a baseball horizontally at 25 meters per second from a cliff 45 meters above the level ground. Approximately how far from the base of the cliff does the ball hit the ground? [neglect air resistance.]

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dsdrajlin

A baseball is thrown horizontally at 25 m/s from a cliff 45 m above the level ground and it hits the ground 75 m from the base of the cliff.

First, we will calculate the time the baseball is in the air by analyzing the vertical movement.

This is a uniformly accelerated motion, where the initial vertical velocity (u) is 0, the displacement (s) is 45 m and the acceleration is that of gravity (a = 9.8 m/s²).

We can calculate the time (t) in the air using the following kinematic equation.

\(s = ut + \frac{1}{2} a t^{2} \\\\45m = (0m/s)t + \frac{1}{2} (9.8m/s^{2} ) t^{2} \\\\t = 3.0 s\)

Horizontally, it travels for 3.0 s at a speed of 25 m/s. The horizontal distance traveled is:

\(3.0s \times \frac{25m}{s} = 75 m\)

A baseball is thrown horizontally at 25 m/s from a cliff 45 m above the level ground and it hits the ground 75 m from the base of the cliff.

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nuhulawal20

Neglecting air resistance, the distance from the base of the cliff where the baseball hit the ground is approximately 75.75m.

Given the data in the question;

  • Initially, the baseball was at rest before it was thrown
  • Initial velocity; \(u = 0m/s\)
  • Final velocity; \(v = 25m/s\)
  • Height of the cliff; \(s = 45m\)

First, we determine the time taken. Using the second equation of motion:

\(s = ut + \frac{1}{2}gt^2\)

Where s is the height of the cliff, u is initial velocity, t is time taken, a is acceleration due to gravity( \(9.8m/s^2\))

We substitute in our values

\(45m = 0 + \frac{1}{2}*9.8m/s^2\ *\ t^2\\\\t = \sqrt{ \frac{45m}{4.9m/s^2}}\\\\t = 3.03s\)

Now, to get the horizontal distance, we simply multiply the velocity of the baseball and time taken

Horizontal distance = \(25m/s\ *\ 3.03s\)

Horizontal distance = \(75.75m\)

Therefore, neglecting air resistance, the distance from the base of the cliff where the baseball hit the ground is approximately 75.75m.

Learn more: https://brainly.com/question/14103880

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