a bomb is dropped from an airplane at an altitude of 14,400 feet. how long will it take to reach the ground? (because of the motion of 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 horizontally after it is released from plane?
The time of fall is dependent on altitude and gravity.
time= sqrt (2*14,400/32)
how far? 600mi/hr= 880ft/sec
multiply that by time.
To determine the time it takes for the bomb to reach the ground, we can use the formula for vertical motion:
\(h = \frac{1}{2}gt^2\)
where:
- \(h\) is the initial altitude (14,400 feet)
- \(g\) is the acceleration due to gravity (32.2 feet per second squared)
- \(t\) is the time in seconds
First, let's convert the initial altitude from feet to meters since the acceleration due to gravity is typically given in meters per second squared:
1 foot = 0.3048 meters
14,400 feet = 4,389.12 meters
Now, let's rearrange the formula to solve for \(t\):
\(t = \sqrt{\frac{2h}{g}}\)
Substituting the values:
\(t = \sqrt{\frac{2(4389.12)}{32.2}}\)
Calculating this:
\(t \approx 27.34\) seconds
Therefore, it will take approximately 27.34 seconds for the bomb to reach the ground.
Now, let's calculate the horizontal distance the bomb will travel after being released from the plane. The distance is given by:
\(d = v \times t\)
where:
- \(d\) is the horizontal distance
- \(v\) is the horizontal velocity (equal to the speed of the plane since the bomb maintains the same horizontal velocity)
- \(t\) is the time in seconds (27.34 seconds)
First, let's convert the speed of the plane from miles per hour to feet per second:
1 mile = 5280 feet
1 hour = 3600 seconds
600 miles per hour = (600 * 5280) / 3600 feet per second
Calculating this:
\(v \approx 880\) feet per second
Now, let's calculate the horizontal distance:
\(d = 880 \times 27.34\)
Calculating this:
\(d \approx 24,004.72\) feet
Therefore, the bomb will travel approximately 24,004.72 feet horizontally after being released from the plane.