Question

In Physics, if you want a water balloon to hit the ground with 584 J of kinetic energy, how high must you drop a 300 g balloon (0.3 kg) from to achieve this on Earth?

A) 8.84 meters
B) 11.73 meters
C) 15.60 meters
D) 20.80 meters

Answer 1

To have the water balloon hit the ground with 584 J of kinetic energy, it must be dropped from a height of approximately 198.64 meters, which does not match any of the provided options.

Step-by-step explanation:

To determine how high you must drop a 300 g (0.3 kg) water balloon to achieve 584 J of kinetic energy when it hits the ground, we use the conservation of energy principle. The gravitational potential energy (PE) at the height from which the balloon is dropped will be equal to the kinetic energy (KE) it has just before it hits the ground, assuming no energy is lost to air resistance or other forces. The formula for gravitational potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s² on Earth), and h is the height.

Solving for h, we have h = KE / (mg). Substituting the given values, we get h = 584 J / (0.3 kg × 9.8 m/s²) = 584 / 2.94 = approximately 198.64 m. Looking at the answer choices provided in the question, none of them are correct since 198.64 m is not an option.