91Ó°ÊÓ

Firstly, we need to express the fundamental principle that underpins this exercise, which is Archimedes' principle of buoyancy: the upward force (buoyant force) that opposes the weight of an immersed object is equal to the weight of the fluid that the object displaces. Symbolically, this principle can be expressed as \( F_{up} = F_{disp} \). However, here we don't talk about forces, but about densities, which are mass divided by volume. If the volumes are the same, we can divide both forces by the common volume and get \( \rho_{obj} g = \rho_{fluid} g \), where \( \rho_{obj} \) is the density of the object (in this case, the block of granite), \( \rho_{fluid} \) is the density of the fluid (here, the peridotite), and \( g \) is the gravitational acceleration. Because the \( g \) is the same on both sides, we can ignore it. We then get: \( \rho_{obj} = \rho_{fluid} \). As the block is partially submerged, it displaces a volume of peridotite equal to the submerged volume, not the total volume of the block. So instead of equal densities, we multiply each side by appropriate distances to express volumes, and get the needed equation: \( \rho_{g} t = \rho_{p} d \), where \( \rho_{g} \) is the density of granite, \( \rho_{p} \) is the density of peridotite, \( t \) is the thickness of a continent, and \( d \) is the depth to which a continent floats in the peridotite.

To calculate the thickness of the continent, we'll re-arrange the equation for \( t \): \( t = \frac{\rho_{p} d}{\rho_{g}} \). We can now substitute the given values: \( t = \frac{3.3 \times 10^{3} kg/m^{3} \times 5.0 km }{2.8 \times 10^{3} kg/m^{3}} \). The units \( kg/m^{3} \) cancel out and with the fact that \( 1 km = 1000 m \), we are left with \( t = 5.0 km \times \frac{3.3}{2.8} \)

Calculate \( 5.0 km \times \frac{3.3}{2.8} \) using a calculator. Remember that the result will be in kilometers due to the remaining units.