Krishna
0

Step 1: According to the given information construct an imaginary figure.

          


          Let P and R be the initial and final positions of the plane respectively

                  Height of the jet plane PQ = RS = 1500 \sqrt{3}

                The angle of elevation of a jet plane from a point A on the ground

                                     \angle PAQ = 60\degree

                The angle of elevation after 15 seconds

                                   \angle RAS = 30\degree


Step 2: Calculate the distance traveled by the plane

              Consider the right triangle APQ

                                        \tan \theta = \frac{opposite}{adjacent} = \frac{PQ}{AQ}


                                       \tan 60\degree = \frac{1500\sqrt{3}}{AQ}


                                             \sqrt{3} = \frac{1500\sqrt{3}}{AQ} ,,,,,,,,,,,,,,,,,,,, ( \because \tan 60\degree = \sqrt{3})


                                           AQ = \frac{1500\sqrt{3}}{\sqrt{3}}


                                            AQ = 1500 m


              Consider the right triangle ARS

                       \tan \theta = \frac{RS}{AS}

                                   \tan 30\degree = \frac{1500\sqrt{3}}{AS}


                                           \frac{1}{\sqrt{3}} = \frac{1500\sqrt{3}}{AS}                  ( \because \tan 30\degree = \frac{1}{\sqrt{3}} )


                                       AS = 1500\sqrt{3}*\sqrt{3}


                                          AS = 1500 * 3

                                          AS = 4500 m

                  From the figure

                  Distance traveled PR = QS =  AS - AQ

                                                              = 4500 - 1500

                                                              = 3000m


Step 3:Find the speed of the  jet plane

            NOTE: Speed = \frac{distance}{time}

                                Time = 15 seconds

                                Distance = 3000 m

                         Speed = \frac{3000}{15}

                                  Speed = 200 \frac{meter}{sec}