A tennis ball is traveling at 20 m/s west and 5 m/s up. What is the overall magnitude of the tennis ball's velocity vector?25 m/s20.6 m/s425 m/s 5 m/s20 m/s
Question
A tennis ball is traveling at 20 m/s west and 5 m/s up. What is the overall magnitude of the tennis ball's velocity vector?
- 25 m/s
- 20.6 m/s
- 425 m/s
- 5 m/s
- 20 m/s
Solution
The magnitude of the velocity vector can be found using the Pythagorean theorem, since the two components of the velocity (20 m/s west and 5 m/s up) are perpendicular to each other.
The Pythagorean theorem is a^2 + b^2 = c^2, where a and b are the two perpendicular components and c is the hypotenuse (in this case, the magnitude of the velocity vector).
So, we substitute the given values into the formula:
(20 m/s)^2 + (5 m/s)^2 = c^2 400 m^2/s^2 + 25 m^2/s^2 = c^2 425 m^2/s^2 = c^2
Taking the square root of both sides to solve for c gives:
c = sqrt(425 m^2/s^2) c = 20.6 m/s
So, the magnitude of the tennis ball's velocity vector is 20.6 m/s.
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