Question

Measurements indicate that boat A has twice the kinetic energy of boat B of the same mass. How fast is boat A traveling if boat B is moving at 34 ​knots? 1 knotequals1 nautical mile per hour​ [nmi/h]; 1 nautical mile ​[nmi]equals​6,076 feet​ [ft].

Answer 1

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 :

$E=\frac{1}{2}mv^2$

Kinetic energy of boat-A is given by :

$E'=\frac{1}{2}mv^2$..[1]

Kinetic energy of boat-B is given by :

$E'=\frac{1}{2}mv'^2$..[2]

E= 2E' (given)

[1] ÷ [2]

$\frac{E}{E'}=\frac{\frac{1}{2}mv^2}{\frac{1}{2}mv'^2}$

$\frac{2E'}{E'}=\frac{v^2}{v'^2}$

$2\times v'^2=v^2$

$2 \times (205,564 ft/hour)^2=v^2$

$8.4513\times 10^{10} ft^2/hour^2=v'^2$

$v'=290,711.4 ft/hour=\frac{290,711.4}{6,076} nautical mile/hour$

v' = 47.84 knots

The speed of the boat-A is 47.84 knots.