Answer :

Final answer:

By separately considering the horizontal and vertical motions of the crate, we can calculate the time of the slide and free-fall respectively, which enables us to determine the height of the table to be approximately 1.00 m.

Explanation:

To solve this problem, we need to recognize that the horizontal and vertical motions of the crate are independent of each other. The crate slides off the table with a horizontal speed of 1.55 m/s and lands 0.7 m away. Since there are no horizontal forces, the horizontal speed remains constant throughout the slide. Meanwhile, the vertical motion is a free-fall, beginning from rest (since the crate starts at the table's edge).

One can use the kinematics equation for the horizontal motion, d = vt, where d is the distance, v is the speed, and t is the time, to find the time it takes for the crate to hit the ground. Rearranging for time gives t = d / v = 0.7m / 1.55 m/s = 0.45 s.

In the vertical motion, we can use the kinematics equation h = 0.5gt², where h is the height, g is the acceleration due to gravity (9.8 m/s²), and t is the time. Plugging in the time gives the height: h = 0.5*(9.8 m/s²)*(0.45 s)² = 1.00 m. Therefore, the height of the table is approximately 1.00 m.

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