Question

A meteorite has a speed of 80.0 m/s when 900 km above the Earth. It is falling vertically (ignore air resistance) and strikes a bed of sand in which it is brought to rest in 3.20 m .

Answer 1

Part a)

`v = 3950.5 m/s`

Part b)

`W = -4.56 * 10^9 J`

Part c)

`F = 1.43 * 10^9 N`

Part d)

`Energy = 4.56 * 10^9 J`

Step-by-step explanation:

Part a)

As we know that total mechanical energy of the meteorite must be conserved

so we will have

`-((6.67 * 10^(-11))(5.98 * 10^(24)))/(6.37 * 10^6 + 9* 10^5) + (1)/(2)(80^2) = -((6.67 * 10^(-11))(5.98 * 10^(24)))/(6.37 * 10^6) + (1)/(2)v^2`

`-5.48 * 10^7 + 3200 = -6.26 * 10^7  + (v^2)/(2)`

`v = 3950.5 m/s`

Part b)

Work done by sand to stop it

`W = \Delta K`

`W = -(1)/(2)mv^2`

`W = -(1)/(2)(585)(3950.5^2)`

`W = -4.56 * 10^9 J`

Part c)

As we know that

W = F. d

so we have

`-4.56 * 10^9 = F * (3.20)`

`F = 1.43 * 10^9 N`

Part d)

Work done = thermal energy

`Energy = 4.56 * 10^9 J`