math question?

Question

A pelican flying in the air over water drops a crab from a height of 30 feet. Th distance the crab is from the water can be represented in the function h(t)= -16t^2+30, where t is time in seconds. To catch the crab as it falls, a gull flies along a path represented by the function g(t)= -8t^2+15. Can the gull catch the crab before it hits the water? If u do answer plz explain. thx

Answer 1

I won't give you the answer so I doubt I will get best answer- but here is what to do:
Find (solve for) t when h(t)=0. that will tell you how long the gull has to get the crab before it hits the water. Take that t and solve for g(t). If at t where h(t)=0 has g(t)>0 the gull will catch the crab before it hits the water

Answer 2

Pelican drops crab from thirty feet. 30 = 16t^2. I get that it will take just under 2.74 seconds for the crab to hit the water. I'm assuming that the gull is starting after the crab from 15'. Logic tells me it just has to open its mouth and catch the thing as it falls. However, if we do the same calculation and say that 15=8t^2 we find it will take the gull 1.37 seconds to reach the water. Either way, the gull gets crabs.

Answer 3

It appears that the gull and the crab will arrive at the water simultaneously in sqrt(15/8) = 1.36931 seconds.

The Pelican drops the crab from 30 feet above the water and the gull starts its dive from 15 feet above the water. By the functions given, they both arrive at the water surface after 1.36931 seconds.