Guide To Archery

Fire Edge

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If I were to fire a bullet straight down from the edge of a cliff that is 16 meters above the ground and it?

hits the ground at a speed of 24m/s, how far above the cliff edge would the bullet have gone if it had been fired straight up?

Working formula is

Vf^2 - Vo^2 = 2gh

where

Vf = velocity at which bullet hits the ground = 24 m/sec. (given)
Vo = initial velocity of bullet
g= acceleration due to gravity = 9.8 m/sec^2 (constant)
h = distance travelled by bullet = 16 m (given)

Substituting appropriate values,

24^2 - Vo^2 = 2(9.8)((16)

Vo^2 = 576 - 313.6 = 262.4

and solving for Vo,

Vo = 16.2 m/sec.

If the bullet were fired straight up, the same working formula is used, i.e.

Vf^2 - Vo^2 = 2gS

where

Vf = final velocity = 0 (when bullet reaches its peak)
Vo = initial velocity =16.2 m/sec (as calculated above)
g = acceleration due to gravity = 9.8 m/sec^2
S = distance travelled if bullet were fired straight up

Substituting values,

0 - (16.2)^2 = 2(-9.8)(S)

NOTE the negative sign attached to the acceleration due to gravity. It simply denotes that the body is slowing down as it is moving up.

Solving for "S"

S = 13.39 m

Hope this helps.

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If I were to fire a bullet straight down from the edge of a cliff that is 16 meters above the ground and it?

hits the ground at a speed of 24m/s, how far above the cliff edge would the bullet have gone if it had been fired straight up?

Working formula is

Vf^2 - Vo^2 = 2gh

where

Vf = velocity at which bullet hits the ground = 24 m/sec. (given)
Vo = initial velocity of bullet
g= acceleration due to gravity = 9.8 m/sec^2 (constant)
h = distance travelled by bullet = 16 m (given)

Substituting appropriate values,

24^2 - Vo^2 = 2(9.8)((16)

Vo^2 = 576 - 313.6 = 262.4

and solving for Vo,

Vo = 16.2 m/sec.

If the bullet were fired straight up, the same working formula is used, i.e.

Vf^2 - Vo^2 = 2gS

where

Vf = final velocity = 0 (when bullet reaches its peak)
Vo = initial velocity =16.2 m/sec (as calculated above)
g = acceleration due to gravity = 9.8 m/sec^2
S = distance travelled if bullet were fired straight up

Substituting values,

0 - (16.2)^2 = 2(-9.8)(S)

NOTE the negative sign attached to the acceleration due to gravity. It simply denotes that the body is slowing down as it is moving up.

Solving for "S"

S = 13.39 m

Hope this helps.

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