The maximum height H of an object launched with Initial velocity v_(0) at an angle Theta is given by the following formula. H=(v_(0)^2sin^2Theta )/(2g) If g=9.8m/s^2 find the height of an object when v_(0)=80m/s and Theta =(3pi )/(5) rad. Do not round any Intermediate computations. Round your answer to the nearest hundredth. H=square m

To find the height of the object, we can use the formula given:<br /><br />$H=\frac {v_{0}^{2}sin^{2}\Theta }{2g}$<br /><br />Given:<br />$v_{0}=80m/s$<br />$\Theta =\frac {3\pi }{5}$ rad<br />$g=9.8m/s^{2}$<br /><br />Substituting the values into the formula, we get:<br /><br />$H=\frac {(80)^{2}sin^{2}\left(\frac {3\pi }{5}\right)}{2(9.8)}$<br /><br />Calculating the value of $sin^{2}\left(\frac {3\pi }{5}\right)$:<br /><br />$sin^{2}\left(\frac {3\pi }{5}\right) = \left(\frac {3\pi }{5}\right)^2$<br /><br />Now, substituting this value back into the formula:<br /><br />$H=\frac {(80)^{2}\left(\frac {3\pi }{5}\right)^2}{2(9.8)}$<br /><br />Simplifying further:<br /><br />$H=\frac {6400\left(\frac {9\pi^2}{25}\right)}{19.6}$<br /><br />$H=\frac {6400\left(\frac {9\pi^2}{25}\right)}{19.6}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac {57600\pi^2}{490}$<br /><br />$H=\frac