### Example Problem: Calculating the Speed of a Ball in Motion**Problem Statement:**Kyle, a 95.0 kg football player, leaps straight up into the air (with no horizontal velocity) to catch a pass. He catches the 0.430 kg ball precisely at the peak of his jump. When he is 0.910 meters off the ground, he hits the ground 0.409 meters away from where he lept. If the ball was moving horizontally when it was caught by Kyle, how fast was the ball traveling?**Answer:**To solve this problem, we need to determine the horizontal speed of the ball when Kyle catches it.1. **Vertical Motion:** Kyle jumps straight up and catches the ball at the peak of his jump when he is 0.910 meters high. We'll denote the following variables: - \( h = 0.910 \) meters (height) - \( g = 9.81 \) meters per second squared (acceleration due to gravity)2. **Time of Flight:** First, we need to find the time it takes for Kyle to fall from his peak height back to the ground: \[ t = \sqrt{\frac{2h}{g}} \] Plugging in the values: \[ t = \sqrt{\frac{2 \times 0.910}{9.81}} \approx 0.43 \text{ seconds} \]3. **Horizontal Motion:** Kyle lands 0.409 meters horizontally from where he jumped: \[ d = 0.409 \text{ meters} \] The horizontal distance traveled by the ball can be determined using the formula for horizontal motion: \[ d = v_{x} \cdot t \] Where: - \( v_{x} \) is the horizontal velocity of the ball Rearranging to solve for \( v_{x} \): \[ v_{x} = \frac{d}{t} = \frac{0.409}{0.43} \approx 0.95 \text{ meters per second} \]Therefore, the horizontal speed of the ball when caught by Kyle was approximately **0.95 m/s**.**Diagrams and Graphs:**There are no diagrams or graphs included in this example problem.

Name: ### Example Problem: Calculating the Speed of a Ball in Motion**Probl
Uploaded: 2024-03-05T11:56:34.000Z
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Description: ### Example Problem: Calculating the Speed of a Ball in Motion**Problem Statement:**Kyle, a 95.0 kg football player, leaps straight up into the air (with no horizontal velocity) to catch a pass. He catches the 0.430 kg ball precisely at the peak of