A ball is rolled horizontally off a table with an initial speed of 4.0 m/s. A stopwatch measures the ball's trajectory time from table to the floor to be 0.34 s. What is the height of the table? (g = 9.8 m/s2 and air resistance is negligible)
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To find the height of the table, we can use the kinematic equation for vertical motion:
h = (1/2) * g * t^2
where h is the height of the table, g is the acceleration due to gravity, and t is the time it takes for the ball to fall.
We are given that the time of the ball's trajectory from the table to the floor is 0.34 seconds, and the acceleration due to gravity is 9.8 m/s^2.
Substituting these values into the equation:
h = (1/2) * (9.8 m/s^2) * (0.34 s)^2
h = (1/2) * (9.8 m/s^2) * (0.1156 s^2)
h = 5.6672 m
Therefore, the height of the table is approximately 5.67 meters.