It happened on the B3081 near Verwood - he had to be cut free by firefighters.
Portsmouth: US Navy Aircraft Arrives
The 100,000-tonne ship USS Theodore Roosevelt and her escort - the destroyer Winston S Churchill - arrive on Sunday for a five-day visit.
Portsmouth is the first port of call on the ships' round-the-world deployment.
The visit forms part of an ongoing partnership between the US and UK on carrier operations in the run-up to the Royal Navy's two new 65,000-tonne ships - HMS Queen Elizabeth and Prince of Wales - entering service.
The Royal Navy's First Sea Lord, Admiral Sir George Zambellas, said: "It is excellent to see US Navy carrier steel in Portsmouth. And in barely two years we will see UK carrier steel here too.
"We warmly welcome the Theodore Roosevelt Carrier Strike Group - a reflection of the close partnership between our nations and navies, and the value of credible seapower in support of our shared national interests.
"Across the spectrum - from Type 45 destroyers providing area air defence for US carriers launching air strikes against ISIL, to generous US support as we regenerate our own carrier strike capability - our common bond has never been richer."
Among the 5,226 crew on board the carrier are six Royal Navy aircraft handlers who are honing their skills ahead of serving on board HMS Queen Elizabeth which is due to arrive in Portsmouth in 2017.
Senior officers on board both ships will call on Royal Navy top brass during the visit to discuss recent global operations and get an update on the UK's carrier programme.
The two navies will also come face-to-face on the football field when a Theodore Roosevelt team face HMS Diamond at HMS Temeraire.
One crew member on board Winston S Churchill particularly looking forward to the visit is 27 year-old Royal Navy officer Lieutenant Lynsey Sewell - the ship's navigating officer. The position is always filled by a UK navigator to honour the ship's British connection.
USS Theodore Roosevelt will anchor off Stokes Bay near Gosport on Sunday at 5pm and the USS Winston S Churchill arrives at Portsmouth Naval Base at approximately 1.30pm. Both leave Portsmouth on March 27.
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