The Canyon Diablo Crater aka the Barringer Crater near Flags

The Canyon Diablo Crater (aka the Barringer Crater) near Flagstaff AZ was created by a meteorite estimated to be -50 m across that struck the Earth about 50,000 years ago. The crater has a diameter of about 1.6 km (-1 mi) and is about 170 m (560 ft) deep. Calculate the impact speed of the meteorite when it struck the Earth. Assume that the meteorite started from rest a very far distance away and travelled straight toward Earth under the gravitational attraction of the Earth.

Solution

conserving energy we have

0=1/2 mv² - GMm/(R+r)

Here m= mass of meteroid

v= impact velocity

M= mass of earth= 5.972 × 10^24 kg

R= radius of earth

r=radius of meteroid

Solving we have,

0.5*v*v=6.67 x 10^-11 m³/(kg sec²)*5.972 × 10^24 kg/(6,371000+25)

=> v= 62522498.3421 m/s