Alice kicks a soccer ball with a mass of 2.1 kg . The ball leaves the ground moving 30 meters per second . What is the kinetic energy of the soccer ball? ( KE =1/2mv^2) 30 J 900J 567 J 945 J

To calculate the kinetic energy of the soccer ball, we can use the formula:<br /><br />\[ KE = \frac{1}{2}mv^2 \]<br /><br />where:<br />- \( KE \) is the kinetic energy,<br />- \( m \) is the mass of the ball,<br />- \( v \) is the velocity of the ball.<br /><br />Given:<br />- \( m = 2.1 \) kg<br />- \( v = 30 \) m/s<br /><br />Now, plug these values into the formula:<br /><br />\[ KE = \frac{1}{2} \times 2.1 \, \text{kg} \times (30 \, \text{m/s})^2 \]<br /><br />First, calculate \( (30 \, \text{m/s})^2 \):<br /><br />\[ (30 \, \text{m/s})^2 = 900 \, \text{m}^2/\text{s}^2 \]<br /><br />Next, multiply this by the mass and the factor \( \frac{1}{2} \):<br /><br />\[ KE = \frac{1}{2} \times 2.1 \, \text{kg} \times 900 \, \text{m}^2/\text{s}^2 \]<br /><br />\[ KE = 1.05 \, \text{kg} \times 900 \, \text{m}^2/\text{s}^2 \]<br /><br />\[ KE = 945 \, \text{J} \]<br /><br />Therefore, the kinetic energy of the soccer ball is \( 945 \) joules. The correct answer is:<br /><br />\[ \boxed{945 \, \text{J}} \]