Question

An airplane of mas $1.50\times {10}^{4}kg$ is in level flight initially moving at $60.0m/s$ the resistive force exerted by air on the airplane has a ,magnitude o f$4.0\times {10}^{4}N$ By Newton's third law, iof the engines exert a force on the exhaust gases to expel them out of the back of the engine, the exhaust gases exerts a force on the engines called thrust, and the value of the thrust in this situation is $7.50\times {10}^{4}N$ Find the speed of the airplane after it has traveled $5.0\times {10}^{2}m$

Answer 1

Given,

mass of airplane is $1.50\times {10}^{4}kg$

initial velocity $\left(v_i\right)$ is $60m/s$

Force exerted by engine $\left(F_e\right)$ is $4\times {10}^{4}N$

Force exerted by air $\left(F_a\right)$ is $7.5\times {10}^{4}N$

Distance $\left(S\right)$ is $5\times {10}^{2}m$

According to newton's second law of motion

$F_{net}=F_e-F_a$

$ma=F_e-F_a$

substitute all value in above equation

$1.5\times {10}^{4}a=4{\times 10}^4-7.5\times {10}^{4}a=\frac{4-7.5}{1.5}m/s^{2}a=2.33m/s^2$

From Newton's law of motion

$V^2=u^2+2as$

Substitute all value in above equation

$V^2={60}^2+2\times 2.33\times 5\times {10}^2{V}^2=3600+2330V=\sqrt{5930}V=77m/s$

hence velocity of airplane after travell distance $S$ is $77m/s$