a bomb is drooped from an airplane at an altitude of 14,400 feet. how long will it take to reach the ground? (Because of the motionof the plane, the fall will not be vertical, but the time will be the same as that for a vertical fall.) the plane is moving at 600 miles per hour. How far will the bomb move more horizontally after it is released from the plane?
Calculus? You have to be kidding.
h=1/2 g t^2
solve for t
horizontaldistance=vi*time
To determine the time it takes for the bomb to reach the ground and the horizontal distance it travels, we can use basic kinematic equations.
First, let's calculate the time it takes for the bomb to reach the ground. Since the fall is not vertical, we need to consider the horizontal motion of the plane. The fact that the time will be the same as that for a vertical fall suggests that we can ignore the horizontal motion. Therefore, we will treat this as a vertical fall scenario.
To solve for the time, we can use the equation of motion for vertical freefall:
h = (1/2) * g * t^2
Where:
h = height
g = acceleration due to gravity (approximately 32.2 ft/s^2)
t = time
Rearranging the equation, we can solve for t:
t = sqrt((2 * h) / g)
Substituting the given height of 14,400 feet:
t = sqrt((2 * 14400) / 32.2)
t ≈ sqrt(900) ≈ 30 seconds
Therefore, it will take approximately 30 seconds for the bomb to reach the ground.
Now, let's calculate the horizontal distance the bomb travels after it is released from the plane. We know that the plane is moving at 600 miles per hour (or mph). To calculate the distance, we need to multiply the horizontal velocity by the time taken.
However, we need to ensure consistent units, so let's convert the velocity to feet per second (fps). Since 1 mile = 5280 feet and 1 hour = 3600 seconds:
600 mph ≈ (600 * 5280) / 3600 fps ≈ 880 fps
Given that the time is 30 seconds, we can calculate the horizontal distance traveled using:
Distance = velocity * time
Distance ≈ 880 fps * 30 seconds
Distance ≈ 26,400 feet
Therefore, the bomb will move approximately 26,400 feet horizontally after it is released from the plane.