Final answer:
Speed is calculated using the Pythagorean theorem on the velocity components. For (Vx, Vy) = (3.8, 8.8) m/sec, the speed is 9.59 m/sec, and for (Vx, Vy) = (75, 35) m/sec, the speed is 82.78 m/sec.
Step-by-step explanation:
Calculating the speed from velocity components requires using the Pythagorean theorem. Specifically, if Vx is the velocity component in the x-direction, and Vy is the velocity component in the y-direction, the speed v can be found using the equation v = √(Vx2 + Vy2).
- For the velocity components (Vx, Vy) = (3.8, 8.8) m/sec, the speed is calculated as: v = √((3.8 m/sec)2 + (8.8 m/sec)2) = √(14.44 + 77.44) = √(91.88) = 9.59 m/sec.
- For the velocity components (Vx, Vy) = (75, 35) m/sec, the speed is: v = √((75 m/sec)2 + (35 m/sec)2) = √(5625 + 1225) = √(6850) = 82.78 m/sec.
The first step is to square each component of the velocity, then sum those squares, and finally take the square root of the sum to find the magnitude of the speed in m/sec.