Questions: You can use these measurement to express the velocity of the puck using component form. For example, if you measured the horizontal velocity as 25 cm/s and the vertical velocity as 50 cm/s, you could write the velocity of the puck like this: v x=25 cm/s v y=50 cm/s You can also express the velocity of the puck in angle-magnitude form. This means you state the magnitude, or amount of the quantity, as well as the direction expressed as an angle. In this case, the magnitude is the velocity in meters per second, and the direction is the angle θ in the image above. Here's how. - to find the magnitude, or amount, of the velocity, you can see from the drawing that the length of the velocity arrow is the hypotenuse of the triangle - Use the Pythagorean theorem to calculate the length of the hypotenuse: v=√(v x+v y^2) Make these calculations using the horizontal and vertical velocities you measured, and enter the value of the velocity here. cm/s

You can use these measurement to express the velocity of the puck using component form. For example, if you measured the horizontal velocity as 25 cm/s and the vertical velocity as 50 cm/s, you could write the velocity of the puck like this: v x=25 cm/s v y=50 cm/s You can also express the velocity of the puck in angle-magnitude form. This means you state the magnitude, or amount of the quantity, as well as the direction expressed as an angle. In this case, the magnitude is the velocity in meters per second, and the direction is the angle θ in the image above. Here's how. - to find the magnitude, or amount, of the velocity, you can see from the drawing that the length of the velocity arrow is the hypotenuse of the triangle - Use the Pythagorean theorem to calculate the length of the hypotenuse: v=√(v x+v y^2) Make these calculations using the horizontal and vertical velocities you measured, and enter the value of the velocity here. cm/s
Transcript text: You can use these measurement to express the velocity of the puck using component form. For example, if you measured the horizontal velocity as $25 \mathrm{~cm} / \mathrm{s}$ and the vertical velocity as $50 \mathrm{~cm} / \mathrm{s}$, you could write the velocity of the puck like this: \[ \begin{array}{l} v x=25^{\frac{\mathrm{cm}}{\mathrm{s}}} \\ v y=50^{\frac{\mathrm{cm}}{\mathrm{s}}} \end{array} \] You can also express the velocity of the puck in angle-magnitude form. This means you state the magnitude, or amount of the quantity, as well as the direction expressed as an angle. In this case, the magnitude is the velocity in meters per second, and the direction is the angle $\theta$ in the image above. Here's how. - to find the magnitude, or amount, of the velocity, you can see from the drawing that the length of the velocity arrow is the hypotenuse of the triangle - Use the Pythagorean theorem to calculate the length of the hypotenuse: $v=\sqrt{v \bar{x}+v v^{2}}$ Make these calculations using the horizontal and vertical velocities you measured, and enter the value of the velocity here. $\mathrm{cm} / \mathrm{s}$
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Solution

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Solution Steps

Step 1: Identify the given components

The horizontal velocity \( v_x \) is given as 25 cm/s, and the vertical velocity \( v_y \) is given as 50 cm/s.

Step 2: Apply the Pythagorean theorem

To find the magnitude of the velocity \( v \), use the Pythagorean theorem: \[ v = \sqrt{v_x^2 + v_y^2} \]

Step 3: Calculate the magnitude

Substitute the given values into the equation: \[ v = \sqrt{(25 \, \text{cm/s})^2 + (50 \, \text{cm/s})^2} \] \[ v = \sqrt{625 + 2500} \] \[ v = \sqrt{3125} \] \[ v \approx 55.9 \, \text{cm/s} \]

Final Answer

The magnitude of the velocity \( v \) is approximately 55.9 cm/s.

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