An Airplane's New Total Speed After Acceleration

What is the airplane's new total speed after 7.0 s?

Final answer: The airplane's new total speed after 7.0 s is 79.06 m/s.

Calculating the New Total Speed of an Airplane

Explanation: To calculate the new total speed of the airplane, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the initial velocity of the airplane represents one side of the triangle, and the acceleration caused by the wind represents the other side. Let's call the initial velocity 'v' and the acceleration 'a'. Using the Pythagorean theorem, we can calculate the magnitude of the new total velocity 'vtotal' as: vtotal = sqrt(v^2 + a^2) Substituting the given values: v = 65.0 m/s (initial velocity) a = 45.0 m/s^2 (acceleration) Plugging these values into the formula, we get: vtotal = sqrt((65.0 m/s)^2 + (45.0 m/s^2)^2) Simplifying the equation: vtotal = sqrt(4225.0 m^2/s^2 + 2025.0 m^2/s^2) vtotal = sqrt(6250.0 m^2/s^2) vtotal = 79.06 m/s Therefore, the airplane's new total speed after 7.0 s is 79.06 m/s.
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