A hawk, flying at a height of 50 feet, spots a rat on the ground. If he dives down to catch the rat at a speed of 45 feet per second, how long will it take him

Question

to catch the rat?

 

The two formulas that you need are:

h = -16t2 + s

h = -16t2 +vt + s

The two formulas that you need are: h = -16t2 + s h = -16t2 +vt + s

Answer 1

s=50

v=-45

h(t) = -16t^2 -45t + 50

set = 0, solve for t

-16t^2 -45t + 50 =0

t = 45/-32 + (1/32)sqr(45^2 +16(4)(50))

=-45/32 + (1/32)sqr(2025 + 3200) = about 0.853 seconds

-16(0.853)^2 -45(0.853) + 50 = -11.641744 - 38.835 + 50 = about 0, rounded off to an integer

it takes a little less than one second to get the rat, if the rat doesn't move.