An airplane of mass 1.3 104 kg is moving at 64 m/s. The pilot then revs up the engine so that the forward thrust by the air around the propeller becomes 7.2 104 N. If the force exerted by air resistance on the body of the airplane has a magnitude of 4.0 104 N, find the speed of the airplane after it has traveled 500 m. Assume that the airplane is in level flight throughout this motion.
To find the speed of the airplane after it has traveled 500 m, we can use the principles of physics.
1. The first step is to calculate the net force acting on the airplane. Net force can be determined using Newton's second law of motion:
Net force = Thrust - Air resistance
Net force = 7.2 x 10^4 N - 4.0 x 10^4 N
2. Once we have the net force, we can calculate the acceleration of the airplane using Newton's second law:
Net force = mass x acceleration
acceleration = Net force / mass
3. Now that we have the acceleration, we can use the equations of motion to calculate the final velocity of the airplane after it has traveled 500 m.
v^2 = u^2 + 2as
where,
v = final velocity
u = initial velocity (64 m/s)
s = distance traveled (500 m)
a = acceleration (calculated in step 2)
4. Rearranging the equation, we get:
v = sqrt(u^2 + 2as)
5. Plug in the values and calculate the final velocity.
Let's calculate the final velocity of the airplane after it has traveled 500 m: