A bullet has a mass of 5g leave a gun at a velocity of 100m/s. What is the kinetic energy of the bullet as it leave the gun? If the gun is fired vertically upwards, how high will the bullet go? (Ignore air resistance and assume g=10m/s2).
KE=1/2 m v^2=1/2 *.05kg*100^2
how high?
PEmax=KEmax
mgh=1/2 m v^2
h=1/2 *100^2 /9.8 m
To find the kinetic energy of a moving object, you can use the formula:
Kinetic Energy = 1/2 * mass * velocity^2
Given:
Mass of the bullet = 5g = 0.005 kg (since 1g = 0.001 kg)
Velocity of the bullet = 100 m/s
Kinetic Energy = 1/2 * 0.005 kg * (100 m/s)^2
Kinetic Energy = 1/2 * 0.005 kg * 10000 m^2/s^2
Kinetic Energy = 250 Joules
Therefore, the kinetic energy of the bullet as it leaves the gun is 250 Joules.
Now, to calculate the maximum height the bullet reaches when fired vertically upwards, we can use the concept of projectile motion.
When the bullet is fired upwards, it gains an initial vertical velocity but gradually slows down due to the force of gravity acting upon it. Eventually, it comes to a stop at its maximum height.
To find the maximum height, we need to determine the time it takes for the bullet to reach its maximum height. We can use the equation for vertical motion:
Final velocity (v) = Initial velocity (u) + acceleration (a) * time (t)
At maximum height, the final velocity is zero, and the acceleration is equal to the acceleration due to gravity, which is -10 m/s^2 (negative direction because it opposes the upward motion).
0 = 100 m/s - 10 m/s^2 * t
Solving for time (t):
10t = 100
t = 100/10
t = 10 seconds
Now, we know it takes 10 seconds for the bullet to reach its maximum height. Using this time, we can calculate the maximum height (H) using the following equation for vertical displacement:
H = Initial velocity (u) * time (t) + 1/2 * acceleration (a) * time^2 (t^2)
H = 100 m/s * 10 s + 1/2 * (-10 m/s^2) * (10 s)^2
H = 1000 m - 500 m
H = 500 meters
Therefore, when the bullet is fired vertically upwards, it will reach a maximum height of 500 meters.