Answer
The speed of the flatcar is $~~1.1~m/s$
Work Step by Step
Let $~~v_i = 5.3~m/s~~$ be the original velocity of the sumo wrestler.
Let $v_f$ be the velocity of the flatcar after the sumo wrestler jumps on it and runs at a velocity of $5.3~m/s$ relative to the flatcar, in the opposite direction from the original direction. Then the velocity of the sumo wrestler is $v_f-5.3~m/s$
We can use conservation of momentum to find the velocity of the flatcar:
$p_f = p_i$
$(242~kg)(v_f-5.3~m/s)+(2140~kg)~v_f = (242~kg)(5.3~m/s)$
$(242~kg)(v_f)+(2140~kg)~v_f = (242~kg)(5.3~m/s)+(242~kg)(5.3~m/s)$
$v_f = \frac{(2) (242~kg)(5.3~m/s)}{(242~kg+2140~kg)}$
$v_f = 1.1~m/s$
The speed of the flatcar is $~~1.1~m/s$
