If we neglect the effects of air resistance,the impact speed of a body of mass m released from rest at an altitude of 2 $\times$ 10⁸ m above the surface of Earth (m_e = 5.99 $\times$ 10²⁴ kg,r_e = 6.37 $\times$ 10⁶ m)is A)~3.92 $\times$ 10⁹ m/s B)~6.26 $\times$ 10⁴ m/s C)~1.10 $\times$ 10⁴ m/s D)~1.21 $\times$ 10⁸ m/s E)None of these is correct.

Question

Quizplus · Accepted Answer

The impact speed can be calculated using the equation v=sqrt(2gh), where g is the gravitational acceleration and h is the height from which the body is released. Plugging in the given values, we get:
g=GM/r^2, where G is the gravitational constant, M is the mass of the Earth, and r is the radius of the Earth.
g=6.67*10^-11*(5.99*10^24)/(6.37*10^6)^2
g=9.81 m/s^2 (approximately)
h=2*10^18 m
v=sqrt(2*9.81*2*10^18)
v=1.097*10^14 m/s
Rounding to two significant figures and expressing in scientific notation, we get:
v=1.1*10^14 m/s
which corresponds to choice C.

If We Neglect the Effects of Air Resistance,the Impact Speed ×\times×

If We Neglect the Effects of Air Resistance,the Impact Speed $\times$