Question

A steel ball with a constant velocity of 0.8m/s rolls off the edge of a table, the table is 0.95m high.How far from the edge of table does the ball land

Answer 1

To determine how far from the edge of the table the ball lands, we need to calculate the time it takes for the ball to fall to the ground and then use that time to find the horizontal distance traveled.

1. **Calculate the time of flight:**
The height of the table is \( h = 0.95 \, \text{m} \). We can use the equation of motion for free fall to find the time it takes to hit the ground:

\[
h = \frac{1}{2} g t^2
\]

where \( g \approx 9.81 \, \text{m/s}^2 \) is the acceleration due to gravity, and \( t \) is the time in seconds. Rearranging the equation gives:

\[
t^2 = \frac{2h}{g}
\]

Substituting the values:

\[
t^2 = \frac{2 \times 0.95}{9.81}
\]

\[
t^2 \approx \frac{1.9}{9.81} \approx 0.1937
\]

\[
t \approx \sqrt{0.1937} \approx 0.439 \, \text{s}
\]

2. **Calculate the horizontal distance traveled:**
Now that we have the time it takes to fall, we can calculate the horizontal distance traveled using the horizontal velocity (\( v_x = 0.8 \, \text{m/s} \)):

\[
\text{Distance} = v_x \times t
\]

Substituting the values:

\[
\text{Distance} = 0.8 \, \text{m/s} \times 0.439 \, \text{s} \approx 0.3512 \, \text{m}
\]

Therefore, the ball lands approximately **0.35 m** from the edge of the table.