Two control towers are located at points Q(-500, 0) and R(500, 0) , on a straight shore where the x-axis runs through (all distances are in meters). At the same moment, both towers sent a radio signal to a ship out at sea, each traveling at 300 m/µs. The ship received the signal from Q 3 µs (microseconds) before the message from R. Find the coordinates (rounded off to two decimal places) of the ship if it is 200 m from the shore (y = 200).
Answers & Comments
DISTANCE
[tex]\normalsize{\blue{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}}}[/tex]
[tex]\large\underline{\mathbb{PROBLEM}:}[/tex]
Two control towers are located at points Q(-500, 0) and R(500, 0) , on a straight shore where the x-axis runs through (all distances are in meters). At the same moment, both towers sent a radio signal to a ship out at sea, each traveling at 300 m/µs. The ship received the signal from Q 3 µs (microseconds) before the message from R. Find the coordinates (rounded off to two decimal places) of the ship if it is 200 m from the shore (y = 200).
[tex]\large\underline{\mathbb{SOLUTION}:}[/tex]
[tex]\sf{The \ coordinates\ are\ x_2 = 202500, y_2 = 47500}[/tex]
[tex]\begin{gathered}\boxed{\begin{array}{ccc} \underline{\rm{Foci:}} \\\\ \sf{Q(-500, \: 0)}\\ \sf{R(500, \: 0)}\\ \sf{Center = (0, \: 0)} \\ \end{array}}\end{gathered}[/tex]
[tex]\begin{array}{ccc} \underline{\rm{Solve:}} \\\\ \sf{C =0-(\text{-}500)}\\ \sf{C = 0+500}\\ \sf{C=500} \\ \end{array}[/tex]
[tex]\begin{array}{ccc} \sf{2a=300(3)}\\\\ \sf{\frac{2a}{2}= \frac{900}{2} }\\\\ \sf{a = 450} \\ \end{array}[/tex]
[tex]\begin{array}{ccc} \underline{\rm{Now:}} \\\\ \sf{b = \sqrt{c^{2} -a^{2}} }\\ \sf{b =\sqrt{(500)^{2} -(450)^{2}} }\\ \sf{b =\sqrt{250,000 -202,500}} \\ \sf{b =\sqrt{47,500}} \\ \end{array}[/tex]
Hence,
[tex]\normalsize{\blue{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}}}[/tex]
#CarryOnLearning
[tex]\rm{\blue{\copyright -NoahBadilla}}[/tex]
Answer:
Two control towers are located at points Q(-500, 0) and R(500, 0) , on a straight shore where the x-axis runs through (all distances are in meters). At the same moment, both towers sent a radio signal to a ship out at sea, each traveling at 300 m/µs. The ship received the signal from Q 3 µs (microseconds) before the message from R. Find the coordinates (rounded off to two decimal places) of the ship if it is 200 m from the shore (y = 200).
Step-by-step explanation:
ano sagot