Final answer:
To find the kinetic energy at the bottom of the wrecking ball's swing, calculate the initial height using trigonometry, then use it to determine the potential energy, which is equal to the kinetic energy at the bottom due to energy conservation.
Step-by-step explanation:
Calculating Kinetic Energy of a Wrecking Ball
To calculate the kinetic energy (KE) at the bottom of its swing for a 125 kg wrecking ball on a 15.4 m cable released from a 33.5° angle, we use the principle of conservation of energy. Initially, the wrecking ball has potential energy (PE) due to its height, which is converted to kinetic energy at the bottom of the swing. The height (h) can be found using trigonometry, h = L - Lcos(θ), where L is the length of the cable and θ is the angle with the vertical. Then, calculate the initial potential energy using PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s²), and h is the height calculated. As there are no energy losses mentioned (such as air resistance), the kinetic energy at the bottom of the swing will equal the initial potential energy.
To find the height: h = 15.4 m - 15.4m × cos(33.5°).
Once h is found, calculate:
PE_initial = m × g × h
Finally, KE_bottom = PE_initial, as energy is conserved.