Question

a flag has a mass of 3.5 kg has a gpe of 255.78 j. at what height is the flagpoles top relative to the ground?

Explanation:

Step1: Recall the formula for gravitational potential energy (GPE)

The formula for GPE is \(GPE = mgh\), where \(m\) is the mass, \(g\) is the acceleration due to gravity (\(g = 9.8\ m/s^{2}\)), and \(h\) is the height.
We need to solve for \(h\), so we can rearrange the formula to \(h=\frac{GPE}{mg}\).

Step2: Substitute the given values into the formula

Given \(m = 3.5\ kg\), \(GPE=255.78\ J\), and \(g = 9.8\ m/s^{2}\).
Substitute these values into \(h=\frac{GPE}{mg}\):
\(h=\frac{255.78}{3.5\times9.8}\)
First, calculate \(3.5\times9.8 = 34.3\).
Then, \(h=\frac{255.78}{34.3}\)
\(h = 7.46\ m\)

Answer:

The height of the flagpole's top relative to the ground is \(7.46\ m\)