12. (10 points) a seal foraging for food in open water drives forward. the path is at an angle tipped below…

12. (10 points) a seal foraging for food in open water drives forward. the path is at an angle tipped below the water - surface. after swimming for 10 min, 240 seconds, the seal is 360 m vertically below the surface. if the initial depth of its dive, calculate the following:\n a. the angle of the seals path below the horizontal surface of the water. make a clear drawing.\n b. the distance the seal swam along its actual path.\n c. the seals speed in m/s.

12. (10 points) a seal foraging for food in open water drives forward. the path is at an angle tipped below the water - surface. after swimming for 10 min, 240 seconds, the seal is 360 m vertically below the surface. if the initial depth of its dive, calculate the following:\n a. the angle of the seals path below the horizontal surface of the water. make a clear drawing.\n b. the distance the seal swam along its actual path.\n c. the seals speed in m/s.

Answer

Explanation:

Step1: Find the angle

We know the vertical distance $y = 360$ m and horizontal distance $x = 920$ m. We use the tangent - function $\tan\theta=\frac{y}{x}$. $\tan\theta=\frac{360}{920}\approx0.3913$ $\theta=\arctan(0.3913)\approx21.3^{\circ}$

Step2: Find the distance along the actual path

We use the Pythagorean theorem $d=\sqrt{x^{2}+y^{2}}$, where $x = 920$ m and $y = 360$ m. $d=\sqrt{920^{2}+360^{2}}=\sqrt{846400 + 129600}=\sqrt{976000}\approx987.9$ m

Step3: Find the speed

The time $t = 240$ s. Speed $v=\frac{d}{t}$. $v=\frac{987.9}{240}\approx4.12$ m/s

Answer:

a. The angle of the seal's path below the horizontal surface of the water is approximately $21.3^{\circ}$. b. The distance the seal swam along its actual path is approximately $987.9$ m. c. The seal's speed is approximately $4.12$ m/s.