Suppose that a ball thrown at a speed of 18 meters per second has a kinetic energy of 230 joules. What will be the kinetic energy (in joules) of the same ball if thrown at 54 meters per second? joules
Suppose that a ball thrown at a speed of 18 meters per second has a kinetic energy of 230 joules. What will be the kinetic energy (in joules) of the same ball if thrown at 54 meters per second? joules
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
Section: Chapter Questions
Problem 1LR
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![**Educational Content: Kinetic Energy Calculation Problem**
**Problem Statement:**
Suppose that a ball thrown at a speed of 18 meters per second has a kinetic energy of 230 joules. What will be the kinetic energy (in joules) of the same ball if thrown at 54 meters per second?
**Solution:**
To solve this problem, we will utilize the formula for kinetic energy:
\[ KE = \frac{1}{2}mv^2 \]
where \( KE \) is the kinetic energy, \( m \) is the mass of the object, and \( v \) is the velocity of the object.
First, we calculate the mass of the ball using the given kinetic energy at 18 m/s:
1. **Initial Kinetic Energy:**
\[ KE_1 = 230 \text{ joules} \]
\[ v_1 = 18 \text{ m/s} \]
Using the formula:
\[ 230 = \frac{1}{2}m(18)^2 \]
\[ 230 = \frac{1}{2}m \times 324 \]
\[ 230 = 162m \]
\[ m = \frac{230}{162} \]
\[ m = 1.42 \text{ kg (approximately)} \]
2. **New Velocity and Kinetic Energy Calculation:**
Now we find the kinetic energy at 54 m/s:
\[ v_2 = 54 \text{ m/s} \]
\[ KE_2 = \frac{1}{2}(1.42)(54)^2 \]
\[ KE_2 = 0.71 \times 2916 \]
\[ KE_2 = 2070.36 \text{ joules (approximately)} \]
Therefore, the kinetic energy of the ball when thrown at 54 meters per second is approximately 2070.36 joules.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45b729a2-d5bd-4f41-91ce-3559b5d6c6a3%2F7c9d0949-0179-4247-87d2-076993625d59%2F55qtifb_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content: Kinetic Energy Calculation Problem**
**Problem Statement:**
Suppose that a ball thrown at a speed of 18 meters per second has a kinetic energy of 230 joules. What will be the kinetic energy (in joules) of the same ball if thrown at 54 meters per second?
**Solution:**
To solve this problem, we will utilize the formula for kinetic energy:
\[ KE = \frac{1}{2}mv^2 \]
where \( KE \) is the kinetic energy, \( m \) is the mass of the object, and \( v \) is the velocity of the object.
First, we calculate the mass of the ball using the given kinetic energy at 18 m/s:
1. **Initial Kinetic Energy:**
\[ KE_1 = 230 \text{ joules} \]
\[ v_1 = 18 \text{ m/s} \]
Using the formula:
\[ 230 = \frac{1}{2}m(18)^2 \]
\[ 230 = \frac{1}{2}m \times 324 \]
\[ 230 = 162m \]
\[ m = \frac{230}{162} \]
\[ m = 1.42 \text{ kg (approximately)} \]
2. **New Velocity and Kinetic Energy Calculation:**
Now we find the kinetic energy at 54 m/s:
\[ v_2 = 54 \text{ m/s} \]
\[ KE_2 = \frac{1}{2}(1.42)(54)^2 \]
\[ KE_2 = 0.71 \times 2916 \]
\[ KE_2 = 2070.36 \text{ joules (approximately)} \]
Therefore, the kinetic energy of the ball when thrown at 54 meters per second is approximately 2070.36 joules.
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