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There are two hares this could be, the savanna hare or the Cape hare (L. capensis). Unfortunately, they are very difficult to tell apart in the field, the Cape hare is larger.
The only thing I can say is that the Serengeti is on the very edge of the savanna hare's distribution but well within that of the Cape hare (the official Serengeti web site lists Cape hare but not savanna hare as being present for what it's worth). Also the savanna hare is more nocturnal, though in this case it looks like the hare has been disturbed whilst resting so that is unlikely to be of any help.
There is a South African iSpot, you could try posting it there:
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