# Projectile Problem: Find Acceleration of Missile to Shoot Down ICBM

• noleguy33
In summary, an ICBM is launched at an angle of 70 degrees and initial speed of 5100 [m/s]. A cruise missile is launched 500 [km] behind the ICBM to intercept it at a height of 1000 [km]. The acceleration of the missile is calculated by using the known values and equations for 1D motion. The logic used to calculate the acceleration is sound, resulting in an answer of 33.3 [m/s].
noleguy33

## Homework Statement

An ICBM is launched from the surface with an initial angle of 70 degrees and initial speed of 5100 [m/s]. 500 [km] behind the launch site a cruise missile is launched to shoot it down at the height of 1000 [km]. Find the acceleration of the missile if it is launched 20 after the ICBM.

Note: the ICBM is a free fall projectile but the missile moves a long a straight line.

## Homework Equations

xf = vi*t + (1/2)at^2/
yf = vi*sin(theta)*t - 4.9t^2

## The Attempt at a Solution

I just want to make sure my logic is correct on this one-

Alright, I know there will be two answers seeing as the ICBM passes y = 1000 [km] twice. And I also know that the missile is going to be considered 1D motion. So, what I did was plug in all of the knowns into the Yf(where Yf = 1000) and get two values for time.

Here is what I did next...

I find the ICBM's DeltaX by using the known angle and side of the ICBM. I then added that DeltaX to the 500km that the missile was behind it. Using Pythagorean theorem(with that answer and the given 1000km), I got the total distance the missile traveled. I plugged into my first equation and with the time(adjusted for the late takeoff) and solved for acceleration. I did the same thing for the second time/location.

I got something like 33.3 [m/s] for the first one... but I'm more interested if my logic is correct.

Thanks!

The first thing that I'm aware is your Xf equation. the initial velocity in x direction should have $$v_i cos(\theta)$$
And an acceleration in that direction is zero.

The Xf equation is for the missile which, from how I interpreted it, 1D movement... i.e., along a straight line.

## 1. What is a projectile problem?

A projectile problem is a type of physics problem that involves calculating the motion of an object that is launched or thrown into the air, such as a missile or a ball.

## 2. What is an ICBM?

An ICBM (Intercontinental Ballistic Missile) is a long-range missile that is capable of delivering nuclear weapons from one continent to another.

## 3. How do you find the acceleration of a missile?

The acceleration of a missile can be found by using the equation a = (vf - vi)/t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time taken for the missile to reach its target.

## 4. Why is it important to find the acceleration of a missile in this scenario?

Finding the acceleration of a missile is important in order to determine if it has enough speed and force to reach and destroy the ICBM. It also helps in predicting the trajectory of the missile and ensuring its accuracy.

## 5. What factors can affect the acceleration of a missile?

The acceleration of a missile can be affected by factors such as the initial velocity, air resistance, gravity, and any external forces acting on the missile. The type and design of the missile can also play a role in its acceleration.

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