Question

The length l (in feet) of runway needed for a small airplane to land is given by l=0.1s^2-3x+22 where s is the airplane's speed (in feet per second). If a pilot is landing a small airplane on a runway 2000 feet long, what s the maximum sped at which the pilot can land?

Answer 1

To find the maximum speed at which the pilot can land on a 2000-foot runway, substitute 2000 for l in the given equation l=0.1s^2-3s+22 and solve for s. The maximum speed is approximately 157.95 feet per second.

Step-by-step explanation:

To find the maximum speed at which the pilot can land, we need to determine the speed at which the length of the runway is equal to 2000 feet.

Given the equation l = 0.1s^2 - 3s + 22, where l is the length of the runway and s is the airplane's speed:

1. Substitute 2000 for l: 2000 = 0.1s^2 - 3s + 22
2. Rearrange the equation: 0.1s^2 - 3s + 22 = 2000
3. Simplify the equation: 0.1s^2 - 3s - 1978 = 0
4. Use the quadratic formula to solve for s:

• s = (-(-3) ± √((-3)^2 - 4(0.1)(-1978))) / (2(0.1))
• s = (3 ± √(9 + 791.2)) / 0.2
• s = (3 ± √800.2) / 0.2
• s ≈ (3 ± 28.29) / 0.2
• s ≈ 157.95 or -142.95

Since speed cannot be negative, the maximum speed at which the pilot can land is approximately 157.95 feet per second.