What is the speed with which the shark's depth is changing?
Final answer: This problem is solved by using trigonometry to break down the shark's movement into horizontal and vertical (depth) components. The rate at which the shark's depth is changing is found to be approximately 9.5 m/s.
Understanding the Shark's Movement
A great white shark is swimming deep beneath the surface of the ocean. The shark sees a seal at the surface and quickly swims diagonally towards it to attack. The shark swims with a speed of 11 m/s at an angle of 65 degrees above the horizontal. This scenario involves vector analysis, where the shark's speed and direction are taken into consideration.
Trigonometry Application
To determine the speed at which the shark's depth is changing, we use trigonometric principles. The speed of the shark can be represented as the hypotenuse of a right triangle, with the horizontal and depth changes as the other two sides. By applying the sine function, we can calculate the depth change. The formula used is: depth change = shark's speed * sin(angle).
Calculation
Substitute the given values into the formula:
Depth change = 11 m/s * sin(65 degrees) = 9.5 m/s approximately.
Therefore, the rate at which the great white shark's depth is changing is 9.5 m/s.
Conclusion
Understanding trigonometry concepts allows us to interpret and analyze complex scenarios like the movement of a great white shark. By breaking down the shark's speed and direction, we can determine the rate at which its depth is changing with precision.