A steel ball is luanched on a table to be 4.0 m/s. If the tabletop is 1.5m tall then where should you place a 20cm tall can to catch the ball where it lands?
Calculate what the x coordinate of the ball would be when it has fallen y = 1.3 m. The ball takes
t = sqrt(2y/g) =0.515 s to get there. It moves 4.0*0.515 = 2.06 m from the table edge in that time.
To find the position where the can should be placed to catch the ball, we need to calculate the horizontal distance the ball will travel before hitting the ground.
First, let's determine the time it takes for the ball to fall from the table to the ground. We can use the equation of motion:
h = (1/2) * g * t^2
Where:
h = height (1.5m)
g = acceleration due to gravity (9.8 m/s^2)
t = time
Rearranging the equation to solve for time, we have:
t = sqrt((2h) / g)
Plugging in the values, we get:
t = sqrt((2 * 1.5) / 9.8) ≈ 0.549 seconds
Now, we can calculate the horizontal distance the ball will travel using the equation of motion:
d = v * t
Where:
d = horizontal distance
v = initial velocity (4.0 m/s)
t = time (0.549 s)
Plugging in the values, we get:
d = 4.0 * 0.549 ≈ 2.196 meters
Therefore, to catch the ball where it lands, you should place the can at a horizontal distance of approximately 2.196 meters from the edge of the table.