A rifle shoots 50.0 gram bullet with a muzzle a velocity of 350 m/s. How fast would a 80.0 kg person have to run in order to have the same amount of kinetic energy as the bullet in flight? If the bullet is shot vertically, what is the the maximum height about the gun barrel reached by the bullet. Ignoring any frictional force.

mv²/2 =MV²/2

V=v•sqrt(m/M) =
=350sqrt(50•10⁻³/80)=
=8.75 m/s
mv²/2=mgh
h= v²/2g=350²/2•9.8 =6250 m

To find the speed at which an 80.0 kg person would have the same kinetic energy as the bullet, we need to equate their kinetic energies. The kinetic energy (KE) of an object is given by the formula:

KE = (1/2) * mass * velocity^2

For the bullet:
Mass = 50.0 grams = 0.050 kg
Velocity = 350 m/s

Substituting these values into the formula, we get:
KE_bullet = (1/2) * 0.050 kg * (350 m/s)^2

Now, let's find the velocity at which the person would have the same kinetic energy. Let's call it v.

KE_person = (1/2) * 80.0 kg * (v^2)

Since we want the kinetic energy of the person to be equal to that of the bullet:
(1/2) * 0.050 kg * (350 m/s)^2 =
(1/2) * 80.0 kg * (v^2)

Simplifying this equation, we find:
(0.025 kg * (350 m/s)^2) / (80.0 kg) = v^2

Now, let's calculate the value of v:
v = sqrt((0.025 kg * (350 m/s)^2) / (80.0 kg))

Using a calculator, we can compute this value to find the speed at which the person would have the same amount of kinetic energy as the bullet.

Now, to determine the maximum height reached by the bullet when shot vertically, we can apply the laws of projectile motion. Ignoring any frictional forces, the vertical motion of the bullet can be considered as free fall under gravity.

The formula to calculate the maximum height (h) reached by an object in free fall under gravity is given by:

h = (v^2) / (2g)

where v is the initial vertical velocity and g is the acceleration due to gravity.

In this case, the initial vertical velocity is zero since the bullet is shot vertically. The only force acting on the bullet is gravity, causing it to decrease its upward velocity and eventually reach zero.

Substituting the values, we can calculate the maximum height:

h = (0 m/s)^2 / (2 * 9.8 m/s^2)

Simplifying, we find:
h = 0 / 19.6 = 0

Therefore, the maximum height reached by the bullet is zero since it doesn't go higher than the gun barrel.