As shown in the figure, a person starts running from a dista...

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As shown in the figure, a person starts running from a distance of from the right edge of a platform with a constant acceleration towards the edge. After leaving the platform, the person lands exactly at the center of the bottom of a truck's carriage. The vertical height from the right edge of the platform to the bottom of the truck's carriage is , and the horizontal distance from the edge of the platform to the center of the carriage is . Assuming , what is the total time of the person's motion?

To determine the total time of the person's motion, we can break the problem into projectile motion and uniformly accelerated motion.

Phase 1: projectile motion

Vertical Motion

The person falls freely after leaving the platform, and the vertical distance they travel is . The only force acting on them in the vertical direction is gravity, and the acceleration due to gravity is .

Using the equation of motion for free fall:

Thus, the time taken to fall to the bottom of the truck's carriage is 0.6 seconds.

Horizontal Motion

During this time, the person covers a horizontal distance of . Since horizontal velocity is constant (there is no horizontal acceleration), we can use the equation:

Solving for :

Phase 2: uniformly accelerated motion

The person starts running from a distance of from the right edge of a platform with a constant acceleration towards the edge.

We can use the kinematic equation to find the acceleration of the person:

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