18. A4 kg bird is flying horizontally with a velocity of 4m/s at a height of 4 m. Calculate the total mechanical energy of the bird. Do 188.8 J 9.8J Do 156.8 J 39.2.

To calculate the total mechanical energy of the bird, we need to consider both its kinetic energy and potential energy.<br /><br />1. Kinetic Energy (KE):<br />The kinetic energy of an object is given by the formula:<br />\[ KE = \frac{1}{2}mv^2 \]<br />where \( m \) is the mass of the object and \( v \) is its velocity.<br /><br />Given:<br />Mass of the bird, \( m = 4 \, kg \)<br />Velocity of the bird, \( v = 4 \, m/s \)<br /><br />Substituting the values into the formula:<br />\[ KE = \frac{1}{2} \times 4 \, kg \times (4 \, m/s)^2 \]<br />\[ KE = \frac{1}{2} \times 4 \, kg \times 16 \, m^2/s^2 \]<br />\[ KE = 2 \times 16 \, J \]<br />\[ KE = 32 \, J \]<br /><br />2. Potential Energy (PE):<br />The potential energy of an object at a height \( h \) is given by the formula:<br />\[ PE = mgh \]<br />where \( g \) is the acceleration due to gravity.<br /><br />Given:<br />Height of the bird, \( h = 4 \, m \)<br />Acceleration due to gravity, \( g = 9.8 \, m/s^2 \)<br /><br />Substituting the values into the formula:<br />\[ PE = 4 \, kg \times 9.8 \, m/s^2 \times 4 \, m \]<br />\[ PE = 156.8 \, J \]<br /><br />3. Total Mechanical Energy (TME):<br />The total mechanical energy is the sum of the kinetic energy and potential energy:<br />\[ TME = KE + PE \]<br />\[ TME = 32 \, J + 156.8 \, J \]<br />\[ TME = 188.8 \, J \]<br /><br />Therefore, the total mechanical energy of the bird is 188.8 J.