You throw the ball from a window that is 9.0 m
 above the ground, at an angle of 14∘
 downward from the horizontal plane. How far from the wall of the house does the ball hit the ground, if its initial speed is 12.3 m/s
? Air resistance is not taken into account.

x=
 

To solve this problem, we can break the initial velocity into horizontal and vertical components and use kinematic equations to find the horizontal distance the ball travels before hitting the ground.

### Given:
- Height of the window: \( y_0 = 9.0 \, \text{m} \)
- Initial speed: \( v_0 = 12.3 \, \text{m/s} \)
- Angle of projection (downward): \( \theta = 14^\circ \)
- Acceleration due to gravity: \( g = 9.8 \, \text{m/s}^2 \)

We can break the velocity into components:
- Horizontal velocity: \( v_{0x} = v_0 \cdot \cos(\theta) \)
- Vertical velocity: \( v_{0y} = v_0 \cdot \sin(\theta) \)

Next, we calculate the time it takes for the ball to hit the ground. Using the vertical motion equation:

\[
y = y_0 + v_{0y}t - \frac{1}{2}gt^2
\]

where:
- \( y = 0 \) (the ground level),
- \( v_{0y} \) is the vertical component of the initial velocity, and
- \( t \) is the time.

We will solve for the time \( t \) first, and then use it to find the horizontal distance \( x \), which is given by:

\[
x = v_{0x} \cdot t
\]

Let me calculate that for you.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can guide you through solving this problem step by step without the calculations. Would you like to proceed that way, or try again later?

Here are some related questions you might explore:
1. How does the angle of projection affect the horizontal distance?
2. What would happen if air resistance was considered?
3. How does changing the height of the window affect the result?
4. What would the time of flight be if the angle were steeper?
5. How would the result change with different initial speeds?

**Tip**: In projectile motion, always decompose the velocity into horizontal and vertical components for easier calculation!

You throw the ball from a window that is 9.0 m above the ground, at an angle of 14∘ downward from the horizontal plane. How far from the wall of the house does the ball hit the ground, if its initial speed is 12.3 m/s? Air resistance is not taken into account.

Solve a projectile motion problem where a ball is thrown from a height of 9.0 m at an angle of 14 degrees downward with an initial speed of 12.3 m/s. Learn how to break the velocity into components and apply kinematic equations to find the horizontal distance. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation