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)

A) 0.11 m
B) 0.22 m
C) 0.33 m
D) 0.44 m
E) 0.57 m

Hint: You don't need to know the horizontal initial velocity to solve this. The vertical distance fallen in time T is (1/2)gT^2

H = 4.9*(0.34)^2 = ___

To solve this problem, we can use the kinematic equation for vertical motion:

h = (1/2)gt^2

Where:
h = height of the table
g = acceleration due to gravity (9.8 m/s^2)
t = time of flight (0.34 s)

To find the height of the table, we need to determine the time it takes for the ball to reach the floor from the table.

Since the ball is rolled horizontally, its initial vertical velocity is zero. This means that the time of flight is the same as the time it takes for the ball to fall to the floor. Therefore, t = 0.34 s.

Now, substitute the given 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 = 0.5684 m

Therefore, the height of the table is approximately 0.57 m.

The correct answer is option E) 0.57 m.

To find the height of the table, we can use the equation for the vertical distance traveled by an object in free-fall:

h = (1/2) * g * t^2

where h is the height, g is the acceleration due to gravity, and t is the time of flight.

Given that the acceleration due to gravity, g, is 9.8 m/s^2 and the time of flight, t, is 0.34 s, we can plug in these values into the equation to find the height of the table.

h = (1/2) * 9.8 * (0.34)^2
h = 0.57 m

Therefore, the height of the table is 0.57 m.

So the correct answer is E) 0.57 m.

0.11m