A student throws a water bottle upward into the air. It takes 1.2 seconds for the bottle to reach it's maximum height. How much time will it take for the water bottle to return to the student's hand
(from its maximum height)?

1.2 seconds

Explanation:

Formula for total time of flight in projectile is; T = 2u/g

Now, for the time to reach maximum height, it is gotten from Newton's first equation of motion;

v = u + gt

t is time taken to reach maximum height.

But in this case, g will be negative since motion is against gravity. Final velocity will be 0 m/s at max height.

Thus;

0 = u - gt

u = gt

t = u/g

Putting t for u/g in the equation of total time of flight, we have;

T = 2t

We are given t = 1.2

Thus, T = 2 × 1.2 = 2.4

Since total time of flight is 2.4 s and time to get to maximum height is 1.2 s, then it means time to fall from maximum height back to the students hand is; 2.4 - 1.2 = 1.2 s

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