Final answer:
The distance a block descends in the y-direction after falling for 1.81 seconds is calculated using the kinematic equation for uniformly accelerated motion under gravity. Assuming initial rest and no initial vertical displacement, the calculation uses the formula y = -1/2gt², resulting in a negative displacement indicating a fall.
Step-by-step explanation:
The question relates to the motion of a block in two dimensions under the influence of gravity. The information given about falling 7.783m in the x implies horizontal motion, but it's not directly related to the distance the block will fall vertically (in the y) just based on the time. For vertical motion, we use the kinematic equations of motion under uniform acceleration due to gravity (g = 9.8 m/s²). The standard equation for vertical displacement y is:
y = y0 + v0t - ½gt²
Assuming the block starts from rest (v0 = 0) and has an initial vertical position of y0 = 0, the vertical displacement y after 1.81 seconds would be calculated as:
y = 0 + 0×1.81 - ½×9.8×1.81²
y = -½×9.8×1.81²
Calculating this gives us the distance the block will descend in the y-direction. Note that the vertical displacement will be negative because it is a descent.