Question

1. an owl has a mass of 4.00 kg. it dives to catch a mouse, losing 800.00 j of its gpe. what was the starting height of the owl, in meters?

Explanation:

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

The formula for gravitational potential energy is \( GPE = mgh \), where \( m \) is the mass, \( g \) is the acceleration due to gravity (we'll use \( g = 9.8\ m/s^2 \)), and \( h \) is the height. We know the mass \( m = 4.00\ kg \), the change in GPE (which is equal to the loss, so \( \Delta GPE = 800.00\ J \)), and we need to find \( h \). Rearranging the formula for \( h \), we get \( h=\frac{GPE}{mg} \).

Step2: Substitute the known values into the formula

Substitute \( m = 4.00\ kg \), \( GPE = 800.00\ J \), and \( g = 9.8\ m/s^2 \) into the formula \( h=\frac{GPE}{mg} \). So we have \( h=\frac{800.00}{4.00\times9.8} \).

Step3: Calculate the value of \( h \)

First, calculate the denominator: \( 4.00\times9.8 = 39.2 \). Then, divide the numerator by the denominator: \( h=\frac{800.00}{39.2}\approx20.41\ m \).

Answer:

The starting height of the owl is approximately \(\boxed{20.4}\) meters (or more precisely \(\boxed{20.41}\) meters depending on the required precision).