[求助]求做空间数学题

cm2316

Captain Zybora is on a routine patrol a few thousand kilometers away from her home space station where the origin of a three dimensional coordinate system is located. (distance are expressed in kilometers) Looking for action, she grins as she she spots an enemy ship. Her display monitor shows that her position is  
P(405,-3201,95). She hits the attack button  on her computer, and her ship begins to travel, starting at t=0, along the attack curve r(t)=(405-t^2)i+(5t-3201)j+(95+t^3)k, where t is in seconds, firing off a projectile at the enemy ship at t=2 seconds. The project travels along a straight line having the same direction as Captain Zybora';s velocity vector at t=2, with a constant acceleration of 4.5(km/s^2). The projectile has an initial speed which is 50km/s faster than Captain Zybora';s speed at the firing time.

Unfortunately, captain Zybora';s computer makes a mistake, and it programs the projectile to explode prematurely 4 seconds after being fired. When the projectile explodes, it will annihilate everything within a 100 kilometers radius, and in the meantime, Captain Zybora has no choice but to continue along the same attack curve for another 5 seconds, before she regains control of her ship. Will she make it? How far from the projectile will she be when it explodes?

captain zybora 在距离空间总站不远的地方巡逻, 空间总站是坐标的原点. (距离按千米为单位) 她发现了一艘敌船. 她的显示器显示她的位置是在P(405,-3201,95)她按了攻击键, 船开始行驶, 从t=0开始, 按着攻击的轨道 r(t)=(405-t^2)i+(5t-3201)j+(95+t^3)k，t=2开火，导弹沿直线，和飞船向同方向，加速度a=4.5，导弹比开火时船快50KM/S
导弹早4S爆炸。爆炸时会消灭r=100范围的东西，船只好沿相同的攻击曲线开5s，当他重新控制时，他离导弹多远。