how high must a 2 kg basketball be thrown so that the top of its arc, it has a potential energy of 160J?
To find the height at which the basketball must be thrown, we can use the equation for potential energy.
The potential energy of an object at a certain height is given by the equation:
Potential Energy (PE) = mass (m) × gravity (g) × height (h)
Given:
Mass of the basketball (m) = 2 kg
Potential energy at the top of the arc (PE) = 160 J
Gravity (g) = 9.8 m/s²
We can rearrange the equation to solve for height:
Height (h) = PE / (m × g)
Substituting the given values into the equation:
h = 160 J / (2 kg × 9.8 m/s²)
h ≈ 8.16 meters
Therefore, the basketball must be thrown to a height of approximately 8.16 meters so that at the top of its arc, it has a potential energy of 160 J.
To determine the height at the top of the arc where the basketball has a potential energy of 160 J, we need to consider the conservation of mechanical energy.
The potential energy (PE) of an object can be calculated using the formula:
PE = mgh,
where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s²), and h is the height above a reference point.
Given that the basketball has a mass of 2 kg and a potential energy of 160 J, we can rearrange the equation to solve for h:
h = PE / (mg).
Substituting in the known values:
h = 160 J / (2 kg * 9.8 m/s²),
h = 8.16 meters.
Therefore, the basketball must be thrown to a height of approximately 8.16 meters so that at the top of its arc, it has a potential energy of 160 J.
M g H = 160 J
Solve for the height H that it rises