Question

Scientists believe that during the Mesozoic period a meteor struck the earth and covered the planet in a layer of sediment which is rich in iridium. This element is not found in abundance on earth, but is commonly found in asteroids. In the study of Spanish soil they found a concentration 30 ng / cm2 of iridium, and let’s assume28that due to the worldwide impact of such a meteor, the layer would be equally as concentrated everywhere on the planet. If needed: the radius of the earth is approximately 6, 371 km and the surface area of a sphere is S = 4πr 2 , where r is its radius.

64. The impact of such a meteor striking the Earth would release a tremendous amount of energy.

(a) The kinetic energy, E, generated by an object is half the product of its mass, m, and the square of its velocity, v. Write this as a mathematical formula.

(b) Does the relationship from part (a) define E as a linear or quadratic function of v (assuming m is held constant)? Does it define E as a linear or quadratic function of m (assuming v is held constant)?

(c) The mass of the asteroid was judged to be approximately 306, 000 Tg (teragrams, billions of kilograms). Letting m be constant at this value, define the function E = g(v) using the formula from part (a) and then graph it on the interval [0, 50000], with v measured in m/s.

(d) In the graph from the previous part, which causes the curve to become steeper, doubling the value of v or doubling the value of m? Relate your answer to the contextual interpretations of v and m.

(e) Estimates put the meteor as moving at 25, 000 m/s. How much energy would the impact of the asteroid generate when it hit the planet? Write this using function notation in addition to finding its value. The units on this answer are written GJ, for gigajoules. (For reference, a 50 megaton nuclear bomb releases an estimated 210,000,000 GJ of energy)

Answer 1