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Question

Pelicans tuck their wings and free fall straight down when diving for fish. Suppose a pelican starts its dive from a height of 16.0m and cannot change its path once committed. If it takes a fish 0.20s to perform evasive action, at what minimum height must it spot the pelican to escape? Assume the fish is at the surface of the water.

Answer 1

x=1/2 a t^2

a = 9.8 m/s^2

16 = 1/2 a t^2

t = 1.8 seconds for pelican to reach 16 feet in freefall

so at 1.6 sec (0.2 sec earlier) x is

1/2 * 9.8 * 1.6^2 = 12.65 meters in descent, or 3.35 m above surface

Answer 2

Vo=0 m/s

Vf=sq.rt. of 2gS

Vf=17.709m/s

t=(Vf-Vo)/g

t=1.8 s

time to get the fish escaped= 1.8s- .20s=1.6s

Vf=Vo+at=0+ 9.8(1.6s)=15.75m/s

minimum height, descent=[(Vf+Vo)/t]=15.75/1.6=9.8 m

The minimum height of descent is 9.8 m. The fish must spot the pelican at the height of 6.2 meters. From 16 meters minus 9.8 meters.

Final answer=6.2 meters above the surface of the water

Answer 3

0.5gt^2 = 16

t = 1.81 secs (time of impact)

Fish must react at t = 1.81 - 0.2 = 1.61

distance travelled by bird in 1.61s = 0.5 (9.81)( 1.61)(1.61) = 12.71m

Minimum height = 16 - 12.71 = 3.29m