Final answer:
A 20.4 kg weight thrown with a velocity of 10 m/s will rise to a height of approximately 5.10 meters before beginning to fall back to the ground, assuming no air resistance and using the conservation of energy principle.
Step-by-step explanation:
How High Will the Weight Go?
To determine how high a 20.4 kg weight thrown with a velocity of 10 m/s will go, we can use the principle of conservation of energy. The kinetic energy (KE) when the weight is thrown will be converted into potential energy (PE) at the peak of its trajectory, where its velocity is zero. The kinetic energy can be calculated using the formula: KE = ½ mv², where m is the mass and v is the velocity. The potential energy at the peak is given by: PE = mgh, where g is the acceleration due to gravity (9.8 m/s²), and h is the height to which the weight rises.
Since KE_initial = PE_peak, we have ½ mv² = mgh. If we solve for height h, we get h = ½ v²/g. Substituting the given values, we get h = ½ (10 m/s)² / (9.8 m/s²) which results in approximately 5.10 meters. This is the height the weight will go before it starts to fall back to the ground.