Question

What is the minimum speed with which a meteor strikes the top of Earth’s stratosphere (about 40.0 km above the surface), assuming that the meteor begins as a bit of interplanetary debris far from Earth and stationary relative to Earth? Assume that the drag force is negligible until the meteor reaches the stratosphere. Mass of Earth is 5.974 × 1024 kg; radius of Earth is 6.371 × 106 m; and gravitational constant is 6.674 × 10−11 N·m2/kg2.

Answer 1

Answer: v = 11149.3 m/s

Step-by-step explanation:

Assuming that the values in your question were supposed to have exponents.

v = minimum speed

r = distance from center of earth

= radius of earth + height above the surface

= (6.371 * 10^6 m) + (0.40 * 10^5 m)

= 6.411 x 10^6 m

M = mass of earth = 5.974 x 10^24 kg

m = mass of meteor

Using conservation of energy

GMm/r = (0.5) m v^2

GM/r = (0.5) v^2

(6.67 * 10^-11)(5.974 * 10^24)/(6.411 * 10^6) = (0.5) v^2

62153455 = (0.5)v^2

Divide both sides by 0.5

124306910 = v^2

Square root both sides

v = 11149.3 m/s