Question

The pirate ship tie at the amusement park is a giant pendulum that riders sit in. It swings back and forth, with a maximum velocity of 20 m/s. If the combined mass of the ride and the passengers is 8000 kg, what is the maximum height of the boat?

Answer 1

Law of conservation of energy states that KE=PE, so

1/2*mv^2=mgh,

1/2*v^2=gh,

h=v^2/2g=20^2/(2*9.8)=20.41 m

Answer 2

Here as we know that there is no loss of energy

so we can say that maximum kinetic energy will become gravitational potential energy at its maximum height

So here we have

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

here we have

v = 20 m/s

m = 8000 kg

now from above equation we have

$\frac{1}{2}(8000)(20^2) = (8000)(9.8)h$

$h = \frac{200}{9.8)$

$h = 20.4 m$

so maximum height is 20.4 m