Let's recall all the necessary formulas. The displacement, Δy, between times t_{1} and t_{2} is : Δy = y_{2} - y_{1}. In order to solve this equation we need values for y1 and y2. Recall the formula: y = y_{0} + v_{0} + gt^{2}/2. We use this formula to solve for the position of the coin at time t_{1}. We take the initial position, y_{0}, to be 0 m, and we take the downward direction to be negative. Because the coin starts at rest, its initial velocity, v_{0}, to be 0 m/s. Therefore, y_{1} = gt_{1}^{2}/2. Plugging in -9.8 m/s^{2} for g, our result is that y_{1} = - 0.59 m.

Now, we just need y_{2}. We can use the same formula y_{2} = y_{1} + v_{1} + gt^{2}/2. We know the values of every variable in this equation except for v_{1}. We can use the following formula to obtain its value: v_{1} = v_{0} + gt_{1}. Remember that the initial velocity is 0 m/s. Solving this equation, we get v_{1} = - 3.40 m/s. Now we can finally solve for y_{2}. The result should be y_{2} = - 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 y_{2} - y_{1} = -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.