Question

• A 50.0 kg circus acrobat drops from a height of 2.0 m straight down onto a springboard with a force constant of 8.00 × 103 N/m. By what maximum distance does she compress the spring?

• Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with a speed of 24.8 m/s independent of the direction thrown.

Answer 1

1.As $U_g=mgh,PE=\frac{1}{2}kx^2$ then from $U_g=PE$ hence $x=\sqrt\frac{2mgh}{k}=\sqrt\frac{2\sdot50\sdot9.8\sdot2}{8\sdot10^3}\approx0.5m$

2.As $mu^2/2=mgh+mv^2/2$ hence $u=\sqrt{2gh+v^2}=\sqrt{2\sdot9.8\sdot20+15^2}\approx24.8m/c$