Final answer:
The mass of the North American continent is calculated as 2.97182 x 10^19 kg based on its volume and density. Its kinetic energy is approximately 1.536 x 10^11 J, given its velocity. A jogger weighing 79kg would need to travel at a speed of roughly 1.75 x 10^6 m/s to have the same kinetic energy.
Step-by-step explanation:
To find the mass of the continent (North American continent), we can use the formula for mass:
Mass = Volume × Density
The volume of the continent is the product of its length, width, and depth: 5450 km × 5450 km × 36 km = 5450 × 5450 × 36 × 10¹¹ m³ (since 1 km = 10³ m).
Therefore, Volume = 1.06524 × 10¹µ m³.
Given the average mass density of the rock is 2790 kg/m³, we then calculate the mass:
Mass = 1.06524 × 10¹µ m³ × 2790 kg/m³ = 2.97182 × 10¹¹ kg.
Next, to find the kinetic energy of the continent, we use the kinetic energy formula:
KE = ½ × mass × velocity²
The continent's velocity is given as 3.2 cm/year, which needs to be converted to meters per second (m/s):
3.2 cm/year = 3.2 × 10⁻² m/year ≈ 1.01587 × 10⁻⁹ m/s (using 1 year = 3.1536 × 10⁷ seconds).
Therefore, KE = ½ × 2.97182 × 10¹¹ kg × (1.01587 × 10⁻⁹ m/s)² ≈ 1.536 × 10¹± J.
For part 3, if the jogger has a mass of 79 kg and the same kinetic energy as the continent, we solve for the speed by rearranging the kinetic energy formula:
½ × m × v² = KE
v = √(2 × KE / m)
v = √(2 × 1.536 × 10¹± J / 79 kg) ≈ 1.75 × 10¶ m/s.
This value represents the speed of the jogger to have the same kinetic energy as the continent.