Respuesta :
Answer:
The speed of the boat-A is 47.84 knots.
Explanation:
Mass of boat-A = m
Mass of boat-B = m
Kinetic energy if the boat-A = E
Kinetic energy if the boat-B = E'
Velocity of boat-A = v = ?
Velocity of boat-B = v'= 34 knots = 34 nautical miles /hour
1 knot = 1 nautical mile per hour
1 nautical mile = 6,076 feet
34 nautical miles /hour = 34 nautical miles /hour × 6,076 ft/miles = 205,564 ft/hour
Kinetic energy of boat-A is given by :
[tex]E=\frac{1}{2}mv^2[/tex]
Kinetic energy of boat-A is given by :
[tex]E'=\frac{1}{2}mv^2[/tex]..[1]
Kinetic energy of boat-B is given by :
[tex]E'=\frac{1}{2}mv'^2[/tex]..[2]
E= 2E' (given)
[1] ÷ [2]
[tex]\frac{E}{E'}=\frac{\frac{1}{2}mv^2}{\frac{1}{2}mv'^2}[/tex]
[tex]\frac{2E'}{E'}=\frac{v^2}{v'^2}[/tex]
[tex]2\times v'^2=v^2[/tex]
[tex]2 \times (205,564 ft/hour)^2=v^2[/tex]
[tex]8.4513\times 10^{10} ft^2/hour^2=v'^2[/tex]
[tex]v'=290,711.4 ft/hour=\frac{290,711.4}{6,076} nautical mile/hour[/tex]
v' = 47.84 knots
The speed of the boat-A is 47.84 knots.
