The plane is flying horizonally at 40m/s at an altitude of 125 m when it drops a bomb. determine how far horizonally from the target you should release the bomb
In the vertical direction this is a plain old falling object problem. How long does it take to fall 125 meters?
125 = (1/2) g t^2
t = sqrt (250/g)
Now how afar does the plane fly and the bomb travel horizontally in t seconds? (Note - unless the plane changes velocity the bomb will land right under the plane. Always pull up in a turn after dropping a bomb.)
d = v t = 40 t
To determine how far horizontally from the target you should release the bomb, we need to consider the horizontal motion of the plane and the vertical motion of the bomb.
Let's assume that the time taken for the bomb to hit the target is the same as the time taken for the bomb to fall vertically from the plane to the ground.
We can use the equation of motion for vertical free fall:
h = (1/2) * g * t^2
Where:
h is the vertical distance traveled by the bomb (125 m in this case)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time taken for the bomb to fall.
Rearranging the equation, we get:
t = sqrt(2h / g)
Substituting the given value of h, we have:
t = sqrt(2 * 125 / 9.8)
t ≈ 5.05 seconds (rounded to two decimal places)
Now, let's calculate the horizontal distance traveled by the plane during this time.
d = v * t
Where:
d is the horizontal distance traveled by the plane
v is the horizontal velocity of the plane (40 m/s in this case)
t is the time taken for the bomb to fall (5.05 seconds)
Substituting the values, we get:
d = 40 * 5.05
d ≈ 202 meters (rounded to two decimal places)
Therefore, to hit the target, you should release the bomb approximately 202 meters horizontally from the target.