What will be the distance from the base of a building where a rock hits the ground if it is thrown horizontally with a speed of 14 m/s from a height of 10 m?

Understand the Problem

The question is asking for the horizontal distance traveled by a rock that is thrown horizontally from a building. It involves understanding projectile motion, specifically how far the rock will travel before it hits the ground, given its horizontal speed and the height from which it is thrown.

Answer

The horizontal distance is calculated using the formula $d = v \cdot \sqrt{\frac{2h}{g}}$.

Steps to Solve

Identify the given values

Assume the height from which the rock is thrown is $h$ meters and the horizontal speed is $v$ meters per second.

Calculate the time to fall

To find out how long the rock takes to hit the ground, we can use the formula for free fall: $$ t = \sqrt{\frac{2h}{g}} $$ Where $g$ is the acceleration due to gravity (approximately $9.81 , \text{m/s}^2$).

Calculate horizontal distance

The horizontal distance $d$ traveled by the rock can be found using the formula: $$ d = v \cdot t $$ By substituting the expression for $t$ from the previous step in this equation: $$ d = v \cdot \sqrt{\frac{2h}{g}} $$

The horizontal distance traveled by the rock is given by the formula $$ d = v \cdot \sqrt{\frac{2h}{g}} $$

More Information

This formula shows how the horizontal distance depends on both the height from which the rock is thrown and its horizontal speed. The rock's horizontal motion is uniform since there is no horizontal acceleration, while the vertical motion is influenced by gravity.

Tips

Forgetting to convert units: Ensure that height is in meters and speed is in meters per second.
Confusing the time of fall with horizontal distance: It's important to separately calculate the time of fall due to gravity before calculating horizontal distance.

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