An arrow is shot vertically upward from a platform 35 ft high at a rate of 166 ft/sec. When will the arrow hit the ground? Ignore the air resistance. Use the formula ℎ = −16 2 + 0 + ℎ0. Round your answer to the nearest tenth.

The arrow will hit the ground approximately 10.5 seconds after launch.

Step-by-step explanation:

The arrow experiments a free fall motion, which is a particular form of uniform accelerated motion due to gravity and in which air friction and effects from Earth's rotation can be neglected. Then, the height as a function of time (), measured in feet, is obtained by the following kinematic formula:

(1)

Where:

- Initial height of the arrow, measured in feet.

- Initial velocity of the arrow, measured in feet per second.

- Time, measured in seconds.

- Gravitational acceleration, measured in feet per square second.

If we know that , , and , then the following polynomial is obtained:

(2)

Lastly, we find the roots of the given expression by the Quadratic Formula:

and

Time is a positive variable and then we conclude that the only solution that is physically reasonable is approximately 10.526 seconds.

The arrow will hit the ground approximately 10.5 seconds after launch.

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