Was the US justified in dropping atomic bombs on Hiroshima and Nagasaki during the Second World...

War is hell.
Longer wars are worse hells.

In answer to the basic question, a resounding YES. Millions of lives saved at the cost of far fewer. Further, Germany and Japan were close to developing their own nuclear weapons and certainly would have used them against the Allies.

The USAAC was burning anywhere from 75000 - 120000 Japanese per night and with the 30 day preliminary bombing approved for the invasion of Japan, the entire citizenship's survival would have been close to extinction. The Japanese Kamikaze's were burning/killing sailors at a horrible rate and the Navy pressured the Army to "do something" or the Navy would have to pull its ships from Okinawa and other areas. The Army's response was to start a horror bombing campaign so scary and fearsome that the Emperor himself would demand that planes husbanded for Kamikaze raids be immediately thrown into air defense. The March 10th firebomb raid was meticulously crafted to occur during a time when Tokyo water supplies would be at a low level and when a lot of your city/infrastructure is wood, that is a lethal combination. The resulting firestorms killed 250000 that we are aware of. Close to a million were made homeless and its possible that an additional 200000 refugees fleeing other bombed cities were killed as well. The premise of the raid was a success and Kamikaze missions fell to one a week, if that.

Additionally, the March raid cost a minimum of 12 bombers of which the majority were ditchings with the crews rescued. Considering the size of the raid (120 bombers or so) and the devastation (close to 75% of the city burned, estimated 500000 dead and code breaking illumination of a million homeless), Colonel Le May's star burned bright and he was green-lighted to repeat the success. Osaka or Nagoya was hit shortly afterwards with 100000+ dead each and large burning percentages. Hiroshima and Nagasaki and two other cities were black listed as they were going to be special weapon targets. The zeal at which Le May's crews were undertaking their planning and execution was proceeding at a speed that put most of Japan to the torch. The raids tailed off with the end of the Okinawa campaign but everyone knew that the Japanese would have "one or two Kamikaze's left" for when the invasion of Japan occurred. So a preliminary aerial bombardment of 30 days was pretty much agreed upon by everyone including British allies who were now gearing up to take part in the invasion from a body bag perspective as well. Mirroring the European model, the USAAC would bomb during the day and the RAF would bomb during the night.

Naval (USN/RN) carrier assets would provide fighter support during the day and roam the countryside looking for targets of opportunity like the P-51's and P-47's of ETO fame. Additionally, RAF and USAAC fighters would soon arrive to also add to the mayhem. "Japan At War" by Edwin Hoyt relays how the roaming fighters mimicked (unintentionally) the Luftwaffe strafing attacks during the Blitz which put so many fleeing refugees to flight, clogging roads and preventing the allies from mounting a credible defense. Bomber raids would then drop leaflets warning of cities to be bombed which then singlehandedly undid the secret police grip on society and soon, masses were evacuating and swamping what little resources Japan had. Sick folk fleeing a city were now in your healthy city causing new sickness like typhoid outbreaks, etc. By the end of day 30, there would more than likely be slim pickings for the recce birds to film. By the second week of USN daylight raiding, the planes were returning with little/few bullet holes and flak damage. Japan was virtually bare. The preliminary bombing missions would be equally successful.

Two atomic bombs saved the Japanese people as a culture and a race. To deny that is to ignore volumes of physical data and actual body counts from the Japanese themselves. We were burning too many people daily. Japan was unable to adequately defend itself. The fire bombs and planes were already East. RAF assets in Singapore had already linked with USAAC scheduling and USAAC fighters from the ETO already had their staffs at Iwo Jima and newly captured Naha/Kadina in Okinawa. The USN already had daily immunity in its sweeps over the countryside. India and Burma would provide support as well. "But why two bombs?" Well...its a long story, but the General who toured Hiroshima post-raid made the following report to the Emperor: "it was an atomic weapon. We know this as we have been working on one ourselves." The Emperor was apprised of Japan's "progress" and one was obviously not available for a reprisal/retaliation. So at this point in time, Japan knows "what" it was. Code breaking then credulously hits high command assertions that "wounded be given weapons and made as comfortable as possible." Hmmm... Time for the second bomb.