Kinematics in 1D: Will Defiance Drake reach the ship or miss?

[CJoy]

Homework Statement

Defiance Drake, Space Adventurer, desperately needs to reach a cargo vessel 100m away, or run out of air and die in deep space. For our purposes, there are two relevant directions, the direction Defiance is traveling in (the x-direction, at 1 m/s), and direction of the cargo ship's motion, which is perpendicular to her motion (y-direction, 10 m/s). Defiance uses her jet boots, choosing to accelerate directly in the x-direction at 0.25g (she starts at (x=100,y=0)). If the cargo vessel is 25 m long, and its nose cone starts at x=0,y=0, will Defiance reach the ship or miss? If she misses, how should she have chosen her path (assume she cannot exceed 1 g)?

Relevant Equations

V(t)=Vo+AoT
X(t)=VoT+1/2AoT

0.25g converts into 2.45m/s^2
V(t)=Vo+AoT
1=0+2.45T
T=1/2.45
T=0.4s
X(t)=VoT+1/2AoT
X(t)=100+0+1/2(2.45)(0.4)^2
X(t)=100.196m
I don't know if this is the right methodology or how to move on from here

 

[scottdave]

I think you misunderstood something. The way I read it, Defiance' initial velocity is 1 m/s, and then accelerates from there. Also, acceleration and velocity carry with them directions. You need to take this into account: for example, is the velocity causing X(t) to increase with time or decrease? What about the acceleration?

Also, what value of time should you use to see if she makes it there in time? Try drawing a picture to help you visualize this.

 

[kuruman]

Also, acceleration and velocity carry with them directions. You need to take this into account: for example, is the velocity causing X(t) to increase with time or decrease? What about the acceleration?

The problem statement is a bit confusing on this. We are told that Defiance's initial velocity and acceleration are in the "x-direction". Does this mean in the positive x-direction following the convention that positive signs are omitted? But then if she starts on the positive x-axis, is initially moving away from the cargo vessel and accelerates also away from it, guess what? If we are to assume that Defiance is not stupid and accelerates in the negative direction towards the cargo vessel (despite the statement of the problem) can we then override the problem once again and assume that her initial velocity is also negative or do we take it as positive?