To determine the speed of an object dropped from a height of 20m when it reaches a height of 5m, we can use the principle of conservation of energy. At any given point during free fall, the potential energy of the object is converted into kinetic energy. We can equate these two energies to find the speed.
The potential energy (PE) of an object at a height h is given by the equation:
PE = m * g * h
Where: m is the mass of the object g is the acceleration due to gravity (approximately 9.8 m/s² on Earth) h is the height above a reference point (in this case, 20m and 5m)
Since the mass of the object cancels out when equating the potential and kinetic energy, we can focus on the heights.
Initially, at a height of 20m, the potential energy is fully converted into kinetic energy when the object reaches a height of 5m.
Using the equation for potential energy, we can write:
PE_initial = m * g * h_initial PE_final = m * g * h_final
The initial potential energy (PE_initial) is equal to the final kinetic energy (KE_final) when the object reaches a height of 5m:
PE_initial = KE_final
m * g * h_initial = 0.5 * m * v_final²
Here, v_final represents the final velocity (speed) of the object when it reaches a height of 5m.
We can rearrange the equation to solve for v_final:
v_final = √(2 * g * h_initial)
Plugging in the values, we have:
v_final = √(2 * 9.8 m/s² * 20m) v_final = √(392 m²/s²) v_final ≈ 19.8 m/s
Therefore, when the object reaches a height of 5m, its speed (velocity) will be approximately 19.8 m/s.