:Question

Two Ships:

Ship P: t=0;r= (20i+ 30j) km, t=3;r= (29i+ 34j) km

Ship Q: t=0;r= (14i- 6j) km andv=12jkmh^-1

at time t hours after midnight, position vectors of P and Q arepandqkm respectively

a) Find velocity of P in terms ofiandj

b) Find expression forpandqin terms of t,iandj

c) at time t hours after midnight, distance between P and Q isdkm

Find expression for PQ to show that

$\displaystyle d^2=25t^2-92t +292$

My answers are as follows:

a) Velocity of P is 3i+8jkmh^-1

b)p= (20+3t)i+ (10+ 8t)j

q= 14i+ (12t-6)j

c) PQ = (3t - 6)i+ (4t -16)j

Therefore $\displaystyle d^2=(3t-6)^2 + (4t-16)^2$

However, This = $\displaystyle 25t^2 - 164t + 292$

Can anyone see where i have gone wrong, or if the question was wrong to start with?