Help!As a bullet falls,it velocity increases until it reaches a maximum value-...

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Gove D

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...this called terminal velocity.? As a bullet falls,it velocity increases until it reaches a maximum value- this called terminal velocity. The magnitude of the bullet's maximum velocity will depend on its size (calibre), whether it tumbles or not and whether it falls nose or blunt end first.

A 2.00g bullet fired from rifle has an initial velocity of 841m/s and travels straight up until it reaches an altitude of 2800m. As it falls, it reaches a terminal velocity of 210m/s.
a) If the rifle has a mass of 3.80kg, what is the recoil velocity of the rifle?
b) how much energy is lost as a result of air resistance as the bullet rises to its maximum altitude?
 
(a) From the law of conservation of mechanical energy :

p(i) = p(f)

Initially, both the bullet and rifle have zero gravitational potential energy as long as the zero point for GPE is taken as the level of the gun and bullet. So the equation becomes :

0 = p(f)
0 = m₁v₁(f) + m₂v₂(f)

Solving for v₂(f) :

v₂(f) = -m₁v₁(f) / m₂
= -(0.002kg)(841m/s) / 3.80kg
= -0.443m/s

(b) The energy lost to air resistance is final PE minus initial KE :

E(lost) = PE(f) - KE(i)
= m₁gh - 0.5vm₁v²
= (0.002kg)(9.80m/s²)(2800m) - 0.5(0.002kg)(841m/s)²
= -652J

Hope this helps.
 
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