Answer to Question #91778 in Mechanics | Relativity for Kina

Question

Johnny Quest is a boy of mass 70 kg. He is standing on a diving board bent 50 cm down and of stiffness 20 kN/m and he is 5 m high above the tranquil waters of the blue lagoon. He is flung into the air by the diving board towards the top of a coconut tree. If he lands at a speed of 3 m/s then find the height of the tree. Assume he does not lose any energy as heat due to drag – the drag is negligible and the efficiency is 100%.

Answer 1

From the law of conservation of energy:

$$kx^2/2+mgh=mu^2/2+mgH$$

m - mass of the boy

k - stiffness

x - bent down of diving board

g - acceleration of gravity(10 m/s^2)

h - height of the diving board

H - height of the tree;

u -boy's speed at the tree

Substituting the values in this formula, we get the answer: H≈8.12m