How far will a block descend in the y-direction after falling in the x-direction?

Calculation for Vertical Descent

The calculation involves using the formula:

y = y0 + v0t - ½gt²

Where:

• y is the vertical displacement
• y0 is the initial vertical position
• v0 is the initial vertical velocity
• t is the time of descent
• g is the acceleration due to gravity (9.8 m/s²)

Assuming the block starts from rest (v0 = 0) and has an initial vertical position of y0 = 0, the equation simplifies to:

y = -½gt²

Plugging in the values for time (1.81 seconds) and acceleration due to gravity, we can calculate the vertical displacement of the block.

Calculating the vertical descent:

y = -½ × 9.8 × (1.81)²

y = -½ × 9.8 × 3.2761

y ≈ -½ × 32.0718

y ≈ -16.0359

Therefore, the distance the block will descend in the y-direction after falling for 1.81 seconds is approximately 16.04 meters. The negative sign indicates that the displacement is in the downward direction, as expected for a descent.