A bullet is shot from the East Coast of the USA and reaches the West Coast of the USA in 4.5 seconds. How fast is that in kilometers per hour?

1 Answer

Answer:

4.5 seconds; #4,173,120(km)/(hr)#

Explanation:

I'm going to tackle this, with a couple of assumptions:

  1. There is no wind resistance, and
  2. There is no bullet deflection (aside from what is needed to deal with the curvature of the Earth - 3240 miles being roughly the distance between the East and West coasts of the USA.

To solve for time in the air, we use:

#s=vt#

We know #s# and #v# so let's solve for #t#:

#3240=720t#

#t=4.5sec#

The velocity of the bullet in #"km"/"hr"# can be found using unit conversions:

#720cancel(mi)/cancel(sec)((3600cancelsec)/(1hr))((1.61km)/(1cancel(mi)))=4,173,120(km)/(hr)#

Just for fun, let's figure out how far that is.

The ISS (International Space Station) is at an altitude of 6371 + 400 = 6771 km from the centre of the Earth (the 6371 is the radius of the Earth and the 400 is the ISS altitude from the surface). Using the circumference of a circle:

#C=2pir#, we can see that the ISS traverses:

#C=2pi(6771)=42543km# and takes roughly an hour and a half (92 minutes).

Our bullet would travel roughly 6,260,000 km in an hour and a half, meaning in the time the ISS orbited the Earth once, the bullet would do so close to 150 times.