Final answer:
To determine the momentum of a 5 kg object falling from a 10 meter height, we calculate its velocity just before impact by converting its potential energy into kinetic energy and then use the velocity to find momentum. The object would have a momentum of approximately 70.7 kg·m/s.
Step-by-step explanation:
The question seems to be asking about the final momentum of an object of mass 5 kg that falls from a certain height, which is incorrectly represented as '10m²'. Nonetheless, we can still calculate the momentum if we assume the height is 10 meters. For the object falling from a height, we would first need to find the velocity of the object just before it hits the ground using the formula for gravitational potential energy (PE = mgh) and then converting that to kinetic energy (KE = ½ mv²) since PE will convert into KE in absence of air resistance.
Assuming g = 10 m/s² for convenience and a height (h) of 10 meters, we can calculate the velocity (v) using the following steps:
- Calculate the potential energy: PE = mgh = 5 kg × 10 m/s² × 10 m = 500 J.
- Assuming no energy loss, all potential energy becomes kinetic energy at the ground: KE = PE = 500 J.
- Using the kinetic energy formula to find v: ½ mv² = KE; therefore, v² = (2 × KE) / m = (2 × 500 J) / 5 kg = 200 m²/s²; thus, v = √200 m²/s² = 14.14 m/s (approximately).
- The momentum (p) of the object is given by p = mv; using the mass of 5 kg and the calculated velocity of 14.14 m/s, p = 5 kg × 14.14 m/s = 70.7 kg·m/s (approximately).