Question

The escape speed from the surface of Planet Zoroaster is 55.0 km/s. The planet has no atmosphere. A meteor far away from the planet moves at speed 4.00 km/s on a collision course with Zoroaster. How fast is the meteor going when it hits the surface of the planet?

Answer 1

Given data

*The escape speed from the surface of Planet Zoroaster is v_1 = 55.0 km/s

*The speed of the meteor is v_2 = 4.00 km/s

The formula for the total energy is given as

`\begin{gathered} E_t=E_1+E_2 \\ (1)/(2)mv^2=(1)/(2)mv^2_1+(1)/(2)mv^2_2 \\ v^2=v^2_1+v^2_2 \\ v=\sqrt[]{v^2_1+v^2_2} \end{gathered}`

Substitute the known values in the above expression as

`\begin{gathered} v=\sqrt[]{(55.0)^2+(4.00)^2} \\ =55.14\text{ m/s} \end{gathered}`