Finding the Mango's Speed Before Impact: A Physics Guide

Let's analyze a mango falling from a tree to understand the physics of free fall motion.The mango starts at a height of 5 meters above the ground.Let's identify our initial conditions. The mango starts from rest at a height of 5 meters, and will fall to the ground at height zero.This is a free fall problem, where the only force acting on the mango is gravity, which accelerates objects at 9.8 meters per second squared.To simplify our analysis, we can ignore air resistance and focus only on gravitational effects.At time equals zero, the mango is at rest, meaning it has no initial velocity.The mango will follow a straight path downward, accelerating due to gravity until it reaches the ground.As the mango falls, its velocity will increase due to gravitational acceleration, while maintaining zero horizontal velocity.To find the mango's final velocity, we'll use the principle of conservation of energy.At the start, all energy is potential energy due to height. As the mango falls, this converts to kinetic energy.The initial potential energy must equal the final kinetic energy.We can write this using the formulas for potential and kinetic energy.Notice that mass appears on both sides of the equation.Since mass is the same on both sides, we can cancel it out, simplifying our equation.Now we can substitute our known values: g equals 9.8 meters per second squared, and h equals 5 meters.This simplified equation gives us everything we need to solve for the final velocity.Now that we have our energy equation, let's solve for the final velocity.First, multiply both sides by 2 to isolate v squared.Then take the square root of both sides to solve for v.Now we can substitute our values: g equals 9.8 meters per second squared, and h equals 5 meters.This simplifies to the square root of 98 meters squared per second squared.Which gives us a final velocity of 9.9 meters per second.To verify our answer makes sense, we can check how long it would take the mango to fall.Using the time equation for free fall, t equals square root of two h over gPlugging in our values gives us approximately 1.01 seconds, which aligns with our velocity calculation.Let's visualize this final velocity just before the mango hits the ground.At the bottom, the mango reaches its maximum speed of 9.9 meters per second.