question : particles A and B are projected vertically upwards with velocities 20m/s and 25m/s. particle B is projected 0.4 seconds later than particle A.
find the velocities of A and B at the instant when the particles are at the same height.
here is my problem: in my book it finds the displacements of both A and B using a suvat formula. and then it equates the two obtained equations (in terms of t ) as follows :
-particle A : s = 20t + 1/2 (-10) t^2 --> -10 for gravity -particle B : s = 25 (t-0.4) + 1/2 (-10) (t-0.4)^2
and then it uses another formula to find velocity of each.
here is my question : as B is projected 0.4 seconds later than A , should it be t+0.4 and not t-0.4?
i really can't wrap my head around it. thanking you in advance for answering.
When $t=0.4$ you want the height that the original function gives at $t=0$, so you evaluate the original function at $t-0.4$ (i.e., indeed at $0.4-0.4=0$ when $t=0.4$)