Question

P. BioLoGY Many birds drop clams or other shellfish in order to break the shell and get the food inside. The time \(t\) (in seconds) it takes for an object such as a clam to fall a certain distance \(d\) (in feet) is given by the equation $$ t=\frac{\sqrt{d}}{4} $$ A gull drops a clam from a height of 50 feet. A second gull drops a clam from a height of 32 feet. Find the difference in the times that it takes for the clams to reach the ground. Round your answer to the nearest hundredth.

Short answer

The difference in the times that it takes for the clams to reach the ground is approximately \(\Delta t = 0.44\) seconds.

Step-by-step solution

Calculate the fall time for the first clam

Insert the first height \(d = 50\) feet into the formula \(t=\frac{\sqrt{d}}{4}\) which results in \(t_1=\frac{\sqrt{50}}{4}\).

Calculate the fall time for the second clam

Insert the second height \(d = 32\) feet into the formula \(t=\frac{\sqrt{d}}{4}\) which results in \(t_2=\frac{\sqrt{32}}{4}\).

Calculate the difference

Subtract the second time from the first time to get the difference: \(\Delta t = t_1 - t_2 = \frac{\sqrt{50}}{4} - \frac{\sqrt{32}}{4}\)

Simplify the difference

Now simplify the expression and round to the nearest hundredth to obtain the final answer.