A gun that shoots bullets at 469m/s is to be aimed at a target 45.7 m away ans level with the gun. How high above the target must the gun barrel be pointed so that the bullet hits the target?
Which equation would I use?
I should have gotten 4.8 cm for the answer...
To solve this problem, we can use the equations of motion to determine the height above the target that the gun barrel should be pointed. The key is to consider both the horizontal and vertical components of the bullet's motion.
First, we can determine the time it takes for the bullet to reach the target horizontally. We can use the equation:
time = distance / horizontal velocity
Substituting the given values, we have:
time = 45.7 m / 469 m/s
Next, we can use the equation of vertical motion to find the height above the target at this time. The vertical motion of the bullet can be described using the equation:
vertical displacement = initial vertical velocity * time - 0.5 * gravity * time^2
In this case, the initial vertical velocity is zero because the bullet is not shot at an upward or downward angle. The value of gravity can be taken as -9.8 m/s^2 (assuming downward direction as negative).
So, the vertical displacement will be:
vertical displacement = 0 * time - 0.5 * (-9.8 m/s^2) * time^2
Now, substitute the value of time obtained earlier and solve for the vertical displacement.
Once you have the vertical displacement, subtract it from the height of the target (assuming that the target is on the ground) to get the height above the target that the gun barrel should be pointed.
Let's calculate:
time = 45.7 m / 469 m/s = 0.0976 s
vertical displacement = 0 * 0.0976 s - 0.5 * (-9.8 m/s^2) * (0.0976 s)^2
vertical displacement = 0 - 0.5 * (-9.8 m/s^2) * 0.00952 s^2
vertical displacement ≈ 0.047 m
Height above the target = 0.047 m = 4.7 cm
Therefore, the correct answer is approximately 4.7 cm, which is close to the 4.8 cm you mentioned.