A small steel ball rolls off a table (1 meter high) with a speed of 2 m/s. Where should they place a can (15 cm high; diameter 10 cm) to catch the ball?
To find the position where the can should be placed to catch the ball, we need to determine the horizontal distance the ball will travel before hitting the ground.
First, let's calculate the time it takes for the ball to reach the ground. We can use the equation for vertical motion:
h = ut + (1/2)gt²
Where:
h = height (1 meter)
u = initial vertical velocity (0 m/s since the ball is rolling horizontally)
g = acceleration due to gravity (-9.8 m/s²)
t = time
Rearranging the equation to solve for time:
t = √(2h/g)
t = √((2 * 1) / 9.8)
t = √(0.204)
t ≈ 0.45 s (rounded to two decimal places)
Next, we can calculate the horizontal distance the ball will travel in this time. We'll use the equation:
d = ut
Where:
d = horizontal distance
u = initial horizontal velocity (2 m/s, given)
t = time (0.45 s)
d = (2 * 0.45)
d ≈ 0.9 m (rounded to one decimal place)
Now, let's determine where to place the can. Since we know the ball will travel a horizontal distance of approximately 0.9 meters, we need to find a position 0.9 meters away from the edge of the table.
Assuming the can should be placed directly under the edge of the table, the can should be placed 0.9 meters away from the vertical line directly beneath the edge.
Therefore, the can should be placed 0.9 meters away from the edge of the table in a straight line beneath it, to catch the ball.