# A missile is released from a fighter plane traveling horizontally at an altitude of 10000 ft. if the target was hit at 2.09 miles, in mi/h, was the plane traveling?

## h = 0.5g*t^2 = 10,000 Ft.

16t^2 = 10,000
t^2 = 625
Tf = 25 s. = Fall time.

V*Tf = 2.09 miles.
V * 25s = 2.09
V = 0.0836 mi/s * 3600s/h = 301 mi/h.

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## Well, let me do some calculations while juggling these numbers. If we convert 10000 ft to miles, it gives us roughly 1.89394 miles. So, we have a distance of 2.09 miles.

Now, to find the time, we need to know at what speed the missile was traveling. Unfortunately, you didn't mention that vital piece of information, so I can't give you an answer. It seems like the plane may have flown away with the speed of mystery or took a speed-boost from a passing unicorn. In either case, it's quite impressive!

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## To determine the speed of the plane in miles per hour (mi/h), we first need to convert the given distances to the same unit.

We know that 1 mile is equal to 5280 feet. Since the target was hit at 2.09 miles, we can convert this distance to feet:
2.09 miles * 5280 feet/mile = 11,011.2 feet

Now, we can calculate the time taken by the missile to travel this distance. Given that the missile is released horizontally and the plane is traveling at a constant speed, the time taken by the missile will be the same as the time taken by the plane.

Next, we need to convert the altitude of the plane from feet to miles. We divide the altitude by 5280 to get the altitude in miles:
10,000 feet / 5280 feet/mile = 1.89394 miles

Now, we can calculate the total distance traveled by the plane:
Total distance = 2.09 miles (distance towards the target) + 1.89394 miles (altitude)
Total distance = 3.98394 miles

Finally, we need to find the time taken by the plane to cover this total distance. We can use the formula: speed = distance/time rearranged to time = distance/speed.
Therefore, time = Total distance / speed

Substituting the known values:
Time = 3.98394 miles / speed

Since we are looking for the speed in mi/h, we rewrite the time in hours, considering that the units will cancel out when divided.

Now, we need to convert the altitude from miles to feet, which will be the same as converting the time from hours to seconds. There are 5280 feet in a mile, and 1 hour consists of 60 minutes and each minute consists of 60 seconds. Therefore, there are 5280 feet/mile * 1 mile/60 minutes * 1 minute/60 seconds = 1.46667 feet/second.

Now, we divide the total distance in miles by the time in hours to obtain the speed in mph:
Time in hours = 3.98394 miles * 1.46667 feet/second / (speed in mph * 5280 feet/mile)
Time in hours = 1.46667 / (speed in mph * 5280)

We can solve the equation by cross-multiplication:
Time in hours * speed in mph * 5280 = 1.46667

Rearranging the equation to solve for speed in mph:
speed in mph = 1.46667 / (Time in hours * 5280)

Since the problem states that the target was hit at 2.09 miles, we can assume that is the total distance traveled. Therefore, substituting this value into the equation:

speed in mph = 1.46667 / ( 2.09 miles * 1.46667 feet/second / (speed in mph * 5280 feet/mile) * 5280)
simplifying,
speed in mph = 1.46667 / ( 2.09 * 5280)
speed in mph ≈ 0.000114579 mph ≈ 0.000115 mph

Therefore, the plane was traveling at approximately 0.000115 mph.

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## To determine the speed of the fighter plane, we need to calculate the time it takes for the missile to reach the target. We can start by converting the given values into a consistent unit.

First, let's convert the altitude of the plane from feet to miles. Since 1 mile is equal to 5280 feet, dividing 10,000 feet by 5280 gives us the altitude in miles:

Altitude (in miles) = 10,000 ft / 5280 ft/mile = 1.893939 mi

Next, we need to convert the distance traveled by the missile from miles to feet. Multiplying 2.09 miles by 5280 gives us the distance in feet:

Distance (in feet) = 2.09 miles * 5280 ft/mile = 11,011.2 ft

Now, let's calculate the time it takes for the missile to reach the target. We can use the concept of time taken by an object in free fall. Neglecting air resistance, the missile will free fall to the same altitude as the target due to gravity. The equation to calculate the time is as follows:

Time = √(2 * height / acceleration due to gravity)

In this case, the height is the difference in altitude between the plane and the target, which is 1.893939 miles. The acceleration due to gravity is approximately 32.174 ft/s^2.

Time = √(2 * 1.893939 mi * 5280 ft/mi / 32.174 ft/s^2)

Simplifying the equation:

Time ≈ √(2 * 1.893939 * 5280 / 32.174) seconds

Calculating the square root and converting seconds to hours (since we want the speed in mi/h):

Time ≈ √(10096.643) seconds ≈ 100.483 seconds ≈ 0.0280236 hours

Finally, to find the speed of the plane in mi/h, we divide the distance by the time:

Speed = Distance / Time

Speed = 11,011.2 ft / (0.0280236 h) ≈ 393,071.4 ft/h ≈ 74.396 mi/h

Therefore, the plane was traveling approximately at 74.396 mi/h.