Answer :
Final answer:
The height of the table is found by using the principles of projectile motion, combining the horizontal distance traveled by the crate with its initial horizontal velocity. Calculations lead to a time of flight of 0.45 seconds and a table height of approximately 0.99 meters, which corresponds to proposal D.
Explanation:
The problem involves calculating the height of the table based on the horizontal distance the crate travels and its initial horizontal velocity. To find the height of the table, we need to use the principles of projectile motion.
The horizontal distance (range) formula for projectile motion is R = (v_0 × t), where v_0 is the initial velocity and t is the time of flight. The time of flight can be determined using the motion in the vertical direction, assuming the only force acting on the crate is gravity (9.81 m/s² downward).
Since the crate falls from the table, the initial vertical velocity (v_y0) is 0 m/s. Using the vertical motion formula y = ½ g t² (where y is the height), we solve for t, substitute it back into the range formula, and finally solve for the height y.
Using the given horizontal distance of 0.7 m and initial horizontal velocity of 1.55 m/s, we find:
The time of flight, t = R / v_0 = 0.7 m / 1.55 m/s = 0.45 s
The height of the table, y = ½ g t² = ½ × 9.81 m/s² × (0.45 s)² = 0.99 m
Therefore, the height of the table is approximately 0.99 m, which corresponds to proposal D.
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