The eye of a hurricane passes over grand bahama island

Asked by admin @ 01/12/2021 in Physics viewed by 256 People

The eye of a hurricane passes over grand bahama island in a direction 60.0Â° north of west with a speed of 41.0 km/h. three hours later the course of the hur- ricane suddenly shifts due north, and its speed slows to 25.0 km/h. how far from grand bahama is the hurri- cane 4.50 h after it passes over the island?

Answered by admin @ 01/12/2021

initial velocity is given as 41 km/h at 60 degree North of West

$v_i = -41 cos60\hat i + 41 sin60 \hat j$

$v_i = -20.5 \hat i + 35.5 \hat j$

After some time the velocity is given as

$v_f = 25 \hat j$

now we can find the acceleration

$a = \frac{v_f - v_i}{t}$

$a = \frac{25\hat j - (-20.5 \hat i + 35.5 \hat j)}{3}$

$a = 6.83 \hat i - 3.5 \hat j$

now the distance is given by

$d = v*t + \frac{1}{2} at^2$

$d = (-20.5 \hat i + 35.5 \hat j)*4.5 + 0.5*(6.83 \hat i - 1.5 \hat j)* 4.5^2$

$d = -92.25\hat i + 159.75\hat j + 69.15\hat i - 15.19\hat j$

$d = -23.1 \hat i + 144.56\hat j$

so the magnitude of distance is

$d = \sqrt{23.1^2 + 144.56^2} = 146.4 km$

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