0.4kg bullet is fired from a gun at a speed of 100 m/s . If the bullet rises straight up into the air, what is the maximum height that the bullet can reach?
max height when starting with velocity v is v^2 / 2g
The mass does not matter.
To find the maximum height that the bullet can reach, we can use the principles of projectile motion. The key concept is that at the highest point of the bullet's trajectory, its vertical velocity is momentarily zero. Using this information, we can calculate the bullet's maximum height.
Step 1: Determine the initial vertical velocity (Vy0).
Since the bullet is fired straight up, the initial vertical velocity is equal to the initial speed (100 m/s), but in the opposite direction because it is moving upward.
Vy0 = -100 m/s
Step 2: Determine the acceleration in the vertical direction (ay).
The acceleration due to gravity on Earth is approximately -9.8 m/s². Since the bullet moves against the force of gravity when moving upward, we use a negative value.
ay = -9.8 m/s²
Step 3: Use the kinematic equation to find the maximum height (h).
The kinematic equation that relates vertical displacement (h), initial vertical velocity (Vy0), vertical acceleration (ay), and time (t) is:
h = Vy0 * t + (1/2) * ay * t²
At the highest point, the final vertical velocity (Vy) is zero. So, we can solve the equation for t when Vy = 0:
0 = Vy0 + ay * t
Solving for t:
t = -Vy0 / ay
Substituting the values of Vy0 and ay:
t = -(-100 m/s) / (-9.8 m/s²)
t = 10.20 s
Now, substituting t back into the original equation to find h:
h = (Vy0 * t) + (1/2) * ay * t²
h = (-100 m/s) * (10.20 s) + (1/2) * (-9.8 m/s²) * (10.20 s)²
Calculating the expression:
h ≈ -1020 m + (-500 m)
h ≈ -1520 m
The negative sign indicates that the calculated height is below the starting point. Therefore, the maximum height reached by the bullet is approximately 1520 meters below its starting point (which is equivalent to its initial height).