Physics Motion Problem (Displacement)

[lp03269]

1. Hi, my question deals with displacement and given acceleration : A boy and a ball are at the top of a ramp. the ball rolls down accelerating at 0.2 m/s(squared). The boy chases after the ball 12 seconds later accelerating at 0.9 m/s(squared). The length of the ramp is 60 meters. Will the boy catch the catch the ball before the end of the ramp, if so what displacement/ time will it be at


2. I was trying to use v2=v1 + aΔt, and manipulate it for the getting the time by after using the equation, Δd=v1Δt+0.5a(Δt)squared



3. My attempt was by trying to divide the displacement by the acceleration and i think i got time(squared) so i square rooted that and than i plugged in the that time by the acceleration to get velocity at that time, and than calculating the displacement by multiplying the velocity by the time. I also tried to substitute the time/ displacement values into each other but i could not balance it out to solve it algebraically. I also tried graphing it and i got my answer somewhere around 15 seconds but I'm not allowed to graph

Any Help would be appreciated... Thanks

 

[mysqlpress]

the total length of ramp = 60 m
So, s= 1/2(0.2)t^2 =0.1t^2
after 12s s' = (0.1)(12)^2=14.4 m
14.4+(0.1)t^2
for the motion of boy
s=1/2(0.9)t^2
combine the equation, find t
if 14.4+(0.1)t^2>=60 it is impossible
<=60 , it is possible