North Korean Intercontinental Ballistic Missiles

North Korean Intercontinental Ballistic Missiles (ICBMs)

Intercontinental missiles are defined to be missiles that travel a distance of greater than 3,418 miles, or 5,500 kilometers. Thus, as the name suggests, they are able to travel substantial distances around the world and even from one continent to another. ICBMs are, in layman's term, guided rockets that propel warheads outside of the Earth's atmosphere and then direct the warhead to the location of its intended detonation.

In recent years, North Korea has placed significant emphasis on the development and testing of weapons of mass destruction; ICBMs and nuclear warheads in particular. These weapons would give North Korea the ability to put the lives of hundreds of thousands of people at risk, all without having to have a single troop set foot in enemy territory. The main target for these weapons, unfortunately, is the United States. For years, North Korea's attempts at developing such weapons were in vain. On July 28, 2017, however, North Korea made its first steps toward achieving this goal. On this date, North Korea successfully launched the Hwasong-14, a missile with the potential of being a fully functional ICBM. Although some experts are doubtful, North Korean officials also asserted that the Hwasong-14 was capable of posing a threat to any region of the United States. To most, this is a very frightening prospect. However, should the capabilities of the Hwasong-14, as given by North Korean officials, be true, it still would not pose a nuclear threat to the United States. This is because North Korea still has another obstacle to overcome; developing a nuclear warhead that is small enough to fit inside the Hwasong-14.

Below is a depiction of North Korea's missiles tests to date: 

Assuming that the missile on Hwasong-14 was launched at an angle of eighty degrees from the horizontal for its trajectory above, does it have the potential to pose a threat to mainland United States? Ignoring air resistance and other factors such as the Earth's atmosphere, use kinematic equations to find out.

Additional information: Data collected by Japanese and South Korean intelligence shows that the missile was in the air for approximately 46 minutes.

Steps:

2300 miles = 3701.49 kilometers

3701.49 kilometers = 3701490 meters

46 minutes = 1380 seconds

To determine the initial velocity, use the data given up to the missiles vertex, or its highest point.

	delta(pos)	Vi	Vf	A	t
X	?	vcos(80)	vcos(80)	0	?
Y	3701490	vsin(80)	?	-9.8	1380

delta(y) = Vi(t) + 1/2At^2

3701490 = vsin(80)(1380) + 1/2(-9.8)(1380)^2

3701490 = v(1359.03) - 9331560

3701490 + 9331560 = v(1359.03)

13033050 = v(1359.03)

13033050 / 1359.03 = v

v = 9589.965

This means that the initial velocity of the Hwasong-14 was 9589.965 m/s. Its maximum range can now be determined by calculating its trajectory when shot at an angle of 45 degrees from the x axis.

	delta(pos)	Vi	Vf	A	t
X	?	9589.965cos(45)	vcos(45)	0	?
Y	0	9589.965sin(45)	?	-9.8	?

delta(y) = Vi(t) + 1/2At^2

0 = 9589.965sin(45)t + 1/2(-9.8)t^2

0 = 6781.13t - 4.9t^2

0 = t (-4.9t + 6781.13)

t = 0, 4.9t = 6781.13

6781.13 / 4.9 = t

t = 1383.9 s

delta(x) = vt

delta(x) = 9589.965cos(45)(1383.9)

delta(x) = 9384404.81 m

The Hwasong-14's maximum range is 9384.40481 km. This means that it is well within the reach of several major cities in the United States.

So, does North Korea pose a nuclear threat to the United States? 

Well, its complicated. Data does seem to show that the Hwasong-14 is capable of reaching California and other parts of mainland United States. However, this is without accounting for air resistance, as well as the added weight of whatever warhead is used.