Projectile Problem: Find Acceleration of Missile to Shoot Down ICBM

[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!

 

[Awatarn]

Your logic looks good.
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.

 

[noleguy33]

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