The energy of a wave is directly proportional to the square of its amplitude. If the initial amplitude of the water wave is 0.5 m and it carries 250 kJ of energy, we can calculate the energy using the formula:
Energy = Amplitude^2
Energy1 = (0.5 m)^2 = 0.25 m^2
Now, if the amplitude at some time later becomes 1.5 m, we can calculate the new energy using the updated amplitude:
Energy2 = (1.5 m)^2 = 2.25 m^2
Therefore, the wave now carries 2.25 times the original energy. To find the exact value in kilojoules (kJ), we can compare the ratios of energy:
Energy2 = Energy1 * (Amplitude2^2 / Amplitude1^2)
Energy2 = 250 kJ * (2.25 m^2 / 0.25 m^2)
Energy2 = 250 kJ * 9
Energy2 = 2250 kJ
So, the wave now carries 2250 kJ of energy.