Question

suppose that a wave forms in shallow water. then the depth d of the water (in meters) and the velocity v of the wave (in meters per second) are related by the equation v = √(9.8d). if a wave formed in shallow water has a velocity of 4.3 meters per second, what is the water’s depth? carry your intermediate computations to at least four decimal places, and round your answer to the nearest tenth.

Explanation:

Step1: Substitute given value into equation

Given $v = \sqrt{9.8d}$ and $v = 4.3$. So, $4.3=\sqrt{9.8d}$.

Step2: Square both sides

$(4.3)^2 = (\sqrt{9.8d})^2$. Since $(\sqrt{a})^2=a$ for $a\geq0$, we get $18.49 = 9.8d$.

Step3: Solve for $d$

$d=\frac{18.49}{9.8}\approx1.8867$.

Step4: Round to nearest tenth

Rounding $1.8867$ to the nearest tenth gives $1.9$.

Answer:

$1.9$