Question 198727
A pelican flying in the air over water drops a crab from a height of 30 feet.
 The distance the crab is from the water as it falls can be represented by 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 + 15.
 Can the gull catch the crab before the crab hits the water? 
:
When the gull catches the crab, they will be at the same height, so we can say:
Gull ht = crab ht
-8t + 15 = -16t^2 + 30
16t^2 - 8t + 15 - 30 = 0
16t^2 - 8t - 15 = 0
Factors to
(4t - 5)(4t + 3) = 0
Positive solution
4t = 5
t = 1.25 sec they will be at the same height (5 ft)
:
A graph would would show this
{{{ graph( 300, 200, -4, 4, -10, 30, -16x^2+30,-8x+15) }}}