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 à 9.8 à (1.81)²
y = -½ à 9.8 à 3.2761
y â -½ à 32.0718
y â -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.