Let's recall all the necessary formulas. The displacement, Δy, between times t1 and t2 is : Δy = y2 - y1. In order to solve this equation we need values for y1 and y2. Recall the formula: y = y0 + v0 + gt2/2. We use this formula to solve for the position of the coin at time t1. We take the initial position, y0, to be 0 m, and we take the downward direction to be negative. Because the coin starts at rest, its initial velocity, v0, to be 0 m/s. Therefore, y1 = gt12/2. Plugging in -9.8 m/s2 for g, our result is that y1 = - 0.59 m.
Now, we just need y2. We can use the same formula y2 = y1 + v1 + gt2/2. We know the values of every variable in this equation except for v1. We can use the following formula to obtain its value: v1 = v0 + gt1. Remember that the initial velocity is 0 m/s. Solving this equation, we get v1 = - 3.40 m/s. Now we can finally solve for y2. The result should be y2 = - 4.47 m. (The negative signs only mean that this position is lower than where we originally started.
Lastly, we just need to calculate Δy. Calculating y2 - y1 = -4.47 - (- 0.59) = - 3.88 m.
Check that this answer makes sense. We expected a negative value for the displacement because the final position of the coin is lower than the initial position.