Two ships are traveling on a straight line in opposite direction, the first ship

Question

Two ships are traveling on a straight line in opposite direction, the first ship is called MAX the other is a star destroyer. MAX computers detect the star destroyer and begins to deaccelerate and just before colliding MAX matches the position and velocity of the star destroyer. If MAX does not deaccelerate they collide in about 30 seconds, they are 100km apart. MAX travels at 10km/s and the star destroyer at 2km/s.

a) Make a position vs time graph of both ships.

b) Find the formulas for velocity and position at the time they meet. Just use Vf, VD,t,a,L for your variables.

C) Find the acceleration magnitude use only Vf,VD,a,L do not use t.

Explanation / Answer

(b) The formulas for velocity and position at the time they meet which is given as :

For velocity, we have

V = a t

For position, we have

L = [Vf + VD] t

If the velocity of max is 10 km/s, then they should collide in (100 km) / (10 km/s + 2 km/s) = 8.33 Sec.

(c) The magnitude of an acceleration which is given as :

using equation of motion 3, we have

Vf2 = VD2 + 2 a L

where, Vf = speed of the MAX = 10 km/s = 10000 m/s

VD = speed of the star destroyer = 2 km/s = 2000 m/s

L = distance travelled = 100 km = 100000 m

then, we get

(10000 m/s)2 = (2000 m/s)2 + 2 a (100000 m)

(100000000 m2/s2) = (4000000 m2/s2) + (200000 m) a

(96000000 m2/s2) = (200000 m) a

a = 480 m/s2

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