9.6.2. Solving a Second-Degree Equation in One Unknown Algebraically and Geometrically

A hawk that was flying at a speed of m/min started landing vertically downwards to attack a snake from a height of m according to the relation ; where is the distance in meters, is the launching speed in meters/minute, and is the time in minutes. Find the time the snake needs to escape before the hawk reaches it.

• A minutes
• B minutes
• C minutes
• D minutes

Example

A hawk that was flying at a speed of m/min started landing vertically downwards to attack a snake from a height of m according to the relation ; where is the distance in meters, is the launching speed in meters/minute, and is the time in minutes. Find the time the snake needs to escape before the hawk reaches it (approximate the result to the nearest tenth if needed).

Solution

If the hawk was flying at a speed of , then the value of is 50 and so the equation becomes

The hawk will reach the snake when the distance travelled is m. Setting equal to 125 gives

This equation can be solved using the quadratic formula

In this example , , , and . Therefore,

As represents time it must have a positive value. Evaluating the positive root and rounding to the nearest tenth gives minutes.

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