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What is the height of the drone in meters above its launching platform that is 5m above the ground, modeled by the equation y = 0.1x^2 - 1.5x + 5, where x is the time in seconds the drone leaves the launch pad, flies down a canyon, and then flies back up again?

Options:
A) 5.1 meters
B) 6.2 meters
C) 7.5 meters
D) 8.8 meters

1 Answer

2 votes

Final answer:

To determine the height of the drone above the launching platform, substitute the time in seconds into the equation y = 0.1x^2 - 1.5x + 5 and solve for y.

Step-by-step explanation:

To find the height of the drone above the launching platform according to the given quadratic equation y = 0.1x^2 - 1.5x + 5, we need to understand that x represents the time in seconds after the drone leaves the launch pad. The equation models the height y (in meters) above the launch pad at any time x. Since the platform is 5 meters above the ground, the height above the ground will be y + 5. However, because the given equation already considers the launch platform height, we can calculate the drone's height above the platform just by using the value of y at time x.

For example, if we wanted to calculate the height of the drone at 1 second, we would substitute x = 1 into the equation:

  • y = 0.1(1)^2 - 1.5(1) + 5
  • y = 0.1 - 1.5 + 5
  • y = 3.6 meters above the launching platform

As none of the provided options (A, B, C, D) correspond to the example calculation for 1 second, we need the specific time x in seconds to perform the correct calculation to find the height of the drone above the platform.

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