I'd love to see an informed response as to why we think they ran instead of hopped. Is there a difference in the skeleton or muscles that would tell us?
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Kangaroos hop because they can store a lot of energy in there Achilles tendon and use that to propel them forward without using much energy. It's good for covering long distances over flat terrain while using as little energy as possible , which is good for the Australian outback as they hop between small patches of vegitation separated by miles of desert. It's not that good for ambushing or quickly chasing prey in a rainforest like the t rex is probably doing.
There's also the issue of scale, a t rex's Achilles tendon would have to be stronger then steel cable and as stretchy as rubber to store and re use that much kinetic force from its weight.
Most likely the weight difference would be the biggest issue here.
Same reason why to scale bug wings wouldn't let you fly, that square cube law can lead to some very unfun conclusions where big beasties are concerned.
Or some absolutely terrifying ones in Shin Godzilla's case.
SQUARE CUBE LAW MENTIONED
I wonder if babies and adolescents hopped around? There's already the theory that T.rexs lived in family groups with adolescents catching lots of small prey and adults catching the occassional large prey and providing protection.
hopping like a kangaroo is unlikely, but it would probably make sense for them to move like modern birds of the same size and whatever is the most similar ecological niche.
Chicky Hopping Baby T-Rexes Cannon!
first off AFAIK they don't even have anything near the amount of muscle in the right places to try hopping, but even if they did manage it i'm pretty sure their legs would snap in half when they landed and then as the rest of the body met the ground they'd crack ribs and stuff as well.
Imagine trying to jump around while wearing a dishwasher on your back, even if you're monstrously strong in every part of your body it's gonna fucking suuuuuuuuck
The math maths
They absolutely did.