Question

1. the largest sea turtle found in the united states had a mass of 860.24 kg. if the gravitational potential energy associated with the turtle as it was being lifted onto a ship was 20,320.7 j, how high above the water was the turtle when it was lifted?

Explanation:

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy is \( PE = mgh \), where \( PE \) is the potential energy, \( m \) is the mass, \( g \) is the acceleration due to gravity (we'll use \( g = 9.8\ m/s^2 \) for this calculation), and \( h \) is the height. We need to solve for \( h \), so we can rearrange the formula to \( h=\frac{PE}{mg} \).

Step2: Substitute the given values into the formula

We know that \( PE = 20320.7\ J \), \( m = 860.24\ kg \), and \( g = 9.8\ m/s^2 \). Plugging these values into the formula for \( h \), we get:
\( h=\frac{20320.7}{860.24\times9.8} \)

Step3: Calculate the denominator first

First, calculate \( 860.24\times9.8 \). Let's do that:
\( 860.24\times9.8 = 860.24\times(10 - 0.2)=860.24\times10 - 860.24\times0.2 = 8602.4 - 172.048 = 8430.352 \)

Step4: Calculate the height

Now, divide the potential energy by the result from the denominator:
\( h=\frac{20320.7}{8430.352}\approx2.41\ m \) (rounded to two decimal places)

Answer:

The turtle was approximately \( \boldsymbol{2.41\ m} \) above the water.