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To determine the unknowns, we need to find the initial horizontal velocity (\(v_{0x}\)) and the initial vertical velocity (\(v_{0y}\)).

Given dataTo determine the unknowns, we need to find the initial horizontal velocity (\(v_{0x}\)) and the initial vertical velocity (\(v_{0y}\)).

Given 
- Initial velocity, \(v_0 = 52.0 \, \text{m/s}\)
- Angle of launch, \(\theta = 70.0^\circ\)

Using trigonometric relationships, we can find \(v_{0x}\) and \(v_{0y}\).

\[ v_{0x} = v_0 \cos(\theta) \]
\[ v_{0y} = v_0 \sin(\theta) \]

First, calculate \(v_{0x}\):

\[ v_{0x} = 52.0 \, \text{m/s} \times \cos(70.0^\circ) \]
\[ v_{0x} = 52.0 \, \text{m/s} \times 0.342 \]
\[ v_{0x} \approx 17.8 \, \text{m/s} \]

Next, calculate \(v_{0y}\):

\[ v_{0y} = 52.0 \, \text{m/s} \times \sin(70.0^\circ) \]
\[ v_{0y} = 52.0 \, \text{m/s} \times 0.940 \]
\[ v_{0y} \approx 48.9 \, \text{m/s} \]

Therefore, the initial horizontal velocity (\(v_{0x}\)) is approximately \(17.8 \, \text{m/s}\) and the initial vertical velocity (\(v_{0y}\)) is approximately \(48.9 \, \text{m/s}\).

Would you like more details or have any questions? Here are some related questions:

1. How do you determine the maximum height reached by the projectile?
2. What is the total time of flight for the projectile?
3. How do you calculate the range of the projectile?
4. What is the velocity of the projectile at the highest point?
5. How would air resistance affect the calculations?

**Tip:** Always resolve the initial velocity into horizontal and vertical components when dealing with projectile motion problems.

A cannonball is launched diagonally with an initial velocity of 52.0 m/s at an angle of 70.0°. Determine all unknowns, including the initial horizontal and vertical velocities.

Learn how to determine the horizontal and vertical components of velocity for a cannonball launched at 70.0° with an initial velocity of 52.0 m/s. This physics problem covers key concepts in trigonometry and projectile motion. Suitable for students in Grades 10-12.

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