Answer to Question #296362 in Mechanics | Relativity for micheal

Question

A body of mass 25kg falls on the ground from a height of 19.6m. The body penetrates into the

ground. Assume the resistance by the ground to penetrate is constant and equal to 4998N.

Take g = 9.8m/s2

.

A. Find the final velocity of the body just before it hits the ground. (8 marks)

B. Calculate the retardation (acceleration) when the body is penetrating the ground.

(7 marks)

C. Find the distance through which the body will penetrate into the ground.

(5 marks)

Answer 1

Given:

$m=25\:\rm kg$

$h=m=19.6\:\rm m$

$F=4998\:\rm N$

$g=9.8\:\rm N/kg$

A. The final velocity of the body just before it hits the ground

$$v=\sqrt{2gh}=\sqrt{2*9.8*19.6}=19.6\:\rm m/s$$

B. The retardation (acceleration) when the body is penetrating the ground

$$a=\frac{F-mg}{m}=\rm \frac{4998\: N}{25\: kg}-9.8\: m/s^2=190\: m/s^2$$

C. The distance through which the body will penetrate into the ground

$$d=\frac{v^2}{2a}=\frac{19.6^2}{2*190}=1.0\:\rm m$$