Question

A stone of 20 g is projected vertically upward with a catapult which rubber called has a force constant of 72 Nm-1, if the tension in the cord at the point of release is 36N find the velocity of projector of the stone and the maximum height attained by the stone

Answer 1

$$x=\frac{F}{k}=\frac{36}{72}=0.5\ m$$

From the conservation of energy:

$$0.5mv^2=0.5kx^2$$

The velocity of projector of the stone:

$$v=x\sqrt{\frac{k}{m}}=0.5\sqrt{\frac{72}{0.02}}=30\frac{m}{s}$$

The maximum height attained by the stone:

$$h=\frac{v^2}{2g}=\frac{30^2}{2(9.8)}=46\ m$$