Jason is practicing his tennis stroke by hitting balls against a wall. The ball leaves his racquet at a height of 87.0 cm above the ground at an angle of 80.0° with respect to the vertical.

 

If the speed of the ball as it leaves the racquet is 29.0 m/s, and if it must travel a distance of 18.8 m before it reaches the wall, what is the vertical component of velocity? Enter a positive value if the ball is upward and a negative value if the ball is downward.

To solve for the vertical component of velocity, we need to determine the initial vertical component of the ball's velocity as it leaves Jason's racquet. The vertical component of velocity, \( v_{y} \), can be found using the initial speed of the ball and the angle of launch.

### Step 1: Understand the problem and the given information
- Initial speed of the ball, \( v = 29.0 \) m/s.
- Angle with respect to the vertical, \( \theta = 80.0^\circ \).
- The ball must travel 18.8 m horizontally before reaching the wall.
- Height above ground: 87.0 cm (not directly needed for finding the vertical component but could be useful in other parts of the problem).

### Step 2: Find the vertical component of the velocity

Given the angle is with respect to the vertical, the vertical component of velocity \( v_y \) can be calculated using:

\[
v_y = v \cdot \cos(\theta)
\]

Substitute the given values:

\[
v_y = 29.0 \cdot \cos(80.0^\circ)
\]

### Step 3: Calculate the vertical component

Let's compute this. We'll use degrees for the cosine function.The vertical component of the ball's velocity as it leaves Jason's racquet is approximately **5.04 m/s** upward.

Would you like to go over more details, or do you have any questions? Here are some related questions you might be interested in:

1. What is the horizontal component of the velocity?
2. How long will it take for the ball to reach the wall?
3. What will be the height of the ball when it reaches the wall?
4. What is the total time the ball stays in the air before hitting the wall?
5. What is the maximum height reached by the ball?

**Tip:** Knowing both the vertical and horizontal components of velocity can help in analyzing the full trajectory of a projectile.

Jason is practicing his tennis stroke by hitting balls against a wall. The ball leaves his racquet at a height of 87.0 cm above the ground at an angle of 80.0° with respect to the vertical. If the speed of the ball as it leaves the racquet is 29.0 m/s, and if it must travel a distance of 18.8 m before it reaches the wall, what is the vertical component of velocity? Enter a positive value if the ball is upward and a negative value if the ball is downward.

Learn how to calculate the vertical component of velocity for a tennis ball hit at an angle with a given speed. Understand the application of trigonometric functions and kinematic equations in projectile motion problems, ideal for students in Grades 10-12.

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