How to prove that when a ball thrown up it has speed of v, when it came down, it is also a speed of v.?

Question

If air resistance is neglected, show (algebraically) that a ball thrown vertically upward with a speed of v will have the same speed, v, when it comes back down to the starting point.

Answer 1

gravitational force..hahahaha

Answer 2

Use conservation of energy.

E i = E f + W n.c.

Since W n.c. is 0 (air resistance is neglected), E i = E f

Set gravitational potential energy = 0 at the ground level.

E i has only kinetic energy.

E i = 1/2 m(v i) ^2

E f also only has kinetic energy

E f = 1/2 m(v f) ^2

so we have 1/2 m(v i) ^2 = 1/2 m(v f) ^2

v i = v f

Keep in mind, though, that this is the magnitude of velocity (speed) and does not take into account direction.

Answer 3

actually it would be -v

vf^2=vi^2+2as

vf^2=vi^2+2as

0^2=vi^2+2(9.8)s

vf^2=0^2+2(9.8)s

-vi^2=19.6s

vf^2=19.6s

-vi^2=19.6(vf^2/19.6)

-vi^2=vf^2

-vi=vf

make it a good day