Final answer:
Using the conservation of energy, the kinetic energy of a soccer ball kicked upwards at 55 km/h is converted into potential energy at the highest point. The calculation reveals that the ball would theoretically reach a height of approximately 119.13 meters, but this answer doesn't match the provided options, suggesting an error in the calculation or the given options.
Step-by-step explanation:
To calculate how high a 0.370 kg soccer ball would go if kicked straight up at 55 km/h, we'll use the principle of conservation of energy, which states that kinetic energy (KE) at the moment of the kick will be equal to the potential energy (PE) at the highest point of the ball's path.
First, we need to convert the speed from km/h to m/s:
55 km/h × (1000 m/1 km) × (1 h/3600 s) = 15.28 m/s
Now, calculate the initial kinetic energy (KE) using the formula KE = 0.5 × mass × velocity2:
KE = 0.5 × 0.370 kg × (15.28 m/s)2
KE = 43.16224 J
Next, using the formula for gravitational potential energy (PE) at the top of its trajectory, PE = m × g × h, we can solve for h (height) by setting KE equal to PE:
43.16224 J = 0.370 kg × 9.81 m/s2 × h
h = 43.16224 J / (0.370 kg × 9.81 m/s2)
h = 119.134579 m
However, none of the options given matches this result, therefore there might be an error in the calculation, units conversion, or the options provided may be incorrect. In a real-world scenario, we would also need to account for air resistance which isn't considered in the idealized physics problem.