Question

1. an airplane with a mass of 50 mg lands on a runway with an initial speed of 80 m/s. a net external force of -3.2 × 10^5 n is required to bring the airplane to rest.

a. convert 50 mg to kilograms.
b. how long does it take for the airplane to come to rest?
c. what is the average deceleration the airplane experiences during the landing?

Explanation:

Step1: Convert mass unit

We know that \(1\space Mg = 10^{3}\space kg\). So for \(m = 50\space Mg\), we have \(m=50\times10^{3}\space kg = 5\times 10^{4}\space kg\).

Step2: Find acceleration using Newton's second law

Newton's second law is \(F = ma\). Given \(F=- 3.2\times10^{5}\space N\) and \(m = 5\times10^{4}\space kg\), we can solve for \(a\):

$$a=\frac{F}{m}=\frac{-3.2\times 10^{5}}{5\times 10^{4}}=-6.4\space m/s^{2}$$

Step3: Find time using kinematic equation

The kinematic equation \(v = v_{0}+at\). The final velocity \(v = 0\), initial velocity \(v_{0}=80\space m/s\) and \(a=-6.4\space m/s^{2}\).

$$0 = 80-6.4t$$

$$6.4t=80$$

$$t=\frac{80}{6.4}=12.5\space s$$

Answer:

a. \(5\times 10^{4}\space kg\)
b. \(12.5\space s\)
c. \(-6.4\space m/s^{2}\)