Answer to Question #258101 in Mechanics | Relativity for David

Question

1.For a body dropped from a height, h, the speed, V,with which it strikes the ground depends only on h

and g and a dimensionless numerical factor. Obtain an expression connecting v, h and g.

Answer 1

$a=g$

$v=gt+v_0$

if $v_0=0$ :

$v=gt$

$h_t=h-gt^2/2$

where h is height at t=0,

h_t is height at moment t

when body strikes the ground:

$h_t=0$

$t=\sqrt{\frac{2h}{g}}$

speed, when body strikes the ground:

$v=g\sqrt{\frac{2h}{g}}=\sqrt{2gh}$