A ball rolls horizontally off a dinner table with an initial speed of 2.45m/s. The ball strikes the floor with a horizontal displacement from the table of 1.3m. Determine the height of the table.
To solve this problem, we need to break the horizontal and vertical motion of the ball into separate components. We can use the kinematic equations to find the height of the table.
First, let's find the time it takes for the ball to hit the floor. We can use the horizontal motion equation:
s = vt
where s is the horizontal displacement (1.3m), v is the horizontal velocity (2.45 m/s), and t is the time it takes for the ball to hit the floor.
1.3m = 2.45 m/s * t
t = 1.3m / 2.45 m/s
t ≈ 0.53 s
Now that we have the time it takes for the ball to hit the floor, we can find the vertical height of the table using the vertical motion equation:
h = 1/2 * g * t^2
where h is the height of the table, g is the acceleration due to gravity (9.81 m/s^2), and t is the time calculated above (0.53 s).
h = 1/2 * 9.81 m/s^2 * (0.53 s)^2
h = 1/2 * 9.81 m/s^2 * 0.2809 s^2
h ≈ 1.38 m
Therefore, the height of the table is approximately 1.38 meters.