help, my physics foundation is bad---1. You are designing an airport for small planes. One kind of airplane that might use this airfield must reach a speed before takeoff of at least 27.8 m/s (100 km/h), and can accelerate at 2.00 m/s². (a) If the runway is 150 m long, can this airplane reach the required speed for take off? (b) If not, what minimum length must the runway have?

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We have an airport runway design problem. A small airplane must reach twenty seven point eight meters per second before takeoff, with an acceleration of two point zero zero meters per second squared. We need to determine if a one hundred fifty meter runway is sufficient, and if not, what minimum length is required. Let's solve part a step by step. First, we identify our given parameters: initial velocity is zero meters per second since the airplane starts from rest, required final velocity is twenty seven point eight meters per second, acceleration is two point zero zero meters per second squared, and the runway length is one hundred fifty meters. We'll use the kinematic equation v final squared equals v initial squared plus two times acceleration times displacement. Now let's calculate the actual speed reached. Using the kinematic equation, v reached squared equals zero squared plus two times two point zero zero times one hundred fifty, which gives us six hundred meters squared per second squared. Taking the square root, we get twenty four point four nine meters per second. Comparing this with the required twenty seven point eight meters per second, we see that twenty four point four nine is less than twenty seven point eight. Therefore, the airplane cannot reach the required takeoff speed on a one hundred fifty meter runway. Now for part b, we need to find the minimum runway length. Using the same kinematic equation, we solve for delta x minimum. Twenty seven point eight squared equals zero squared plus two times two point zero zero times delta x minimum. This gives us seven hundred seventy two point eight four equals four point zero zero times delta x minimum. Solving for delta x minimum, we get one hundred ninety three point two one meters. So the answers are: part a, no, the one hundred fifty meter runway is insufficient, and part b, the minimum runway length required is one hundred ninety three point two one meters. To summarize what we've learned: We used the kinematic equation to analyze runway requirements for aircraft takeoff. The one hundred fifty meter runway is insufficient as the airplane only reaches twenty four point four nine meters per second. We calculated that a minimum runway length of one hundred ninety three point two one meters is needed for safe takeoff. This demonstrates how physics principles are essential for designing safe airport infrastructure.