Late one night, a large meteorite strikes in the Kalahari Desert, creating an en

Question

Late one night, a large meteorite strikes in the Kalahari Desert, creating an enormous crater one mile wide. An amateur video of the impact indicates the meteorite was traveling at close to 855.0 m/s and struck the ground at an angle of = 61.0°, as depicted on the right. Unfortunately, the meteorite exploded on impact and only a small portion of the fragments are recovered The size of the meteroite i important to the government of Botswana which wants to use the publicity to attract tourists to the meteor site They have called on you to provide support for their argument that the Kalahari Crater was caused by a meteorite the size of a school bus Others suggest it was closer to the size of a VW bug Fragments collected from the site indicate the meteorite was composed of nickel-iron, with a density of 5250.0 kg/m3. The scientific literature indicates that for such speeds the coefficient of drag(the Greek letter gamma) for meteorites is typically 0.900. According to meterologists, the density of air in the region was 1.18 kg/m3 at the time of impact. To reassure the government, calculate the diameter of the meteorite Assume it was roughly spherical and traveling at terminal velocity Number Im Government scientists in neighboring South Africa protest your results, suggesting that the meteorite had not yet reached terminal velocity when it impacted the Earth's surface. Which of the following would be an accurate response

Explanation / Answer

Drag force=CA rho1 v^2 /2

= C pi r ^2 rho air *v^2 /2

weight = rho steel*4/3 pi r^3 *g

At terminal velocity, forces are balanced, a component of weight will balance dtag force.

    rho steel *4/3*pir^3 *g sin theta = C pi r ^2 rho air *v^2 /2

       5250*4/3*r*9.8 sin 61 degree = 0.9*1.18*855^2 /2

            d = 2r = 0.9*1.18*855^2*3/(4*5250*9.8*sin 61 degree )

           = 12.94 m answer

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