Answer
(a) The gravitational force on the Earth due to the plane is $3.0~kN$
(b) The acceleration of the sailplane is $6.5~m/s^2$ downward.
Work Step by Step
(a) Since the vertical component of acceleration is zero, then the net vertical force must also be zero. Therefore, the gravitational force pulling down on the plane must be equal in magnitude to the upward force of $3.0~kN$.
Since the gravitational force on the plane due to the Earth is $3.0~kN$, by Newton's third law, the gravitational force on the Earth due to the plane is $3.0~kN$
(b) We can find the mass of the plane:
$mg = 3.0~kN$
$m = \frac{3000~N}{9.8~m/s^2}$
$m = 306~kg$
The gravitational force on the plane is $3.0~kN$. If the upward force is only $1.0~kN$, the net force on the plane is $2.0~kN$ directed downward. We can find the acceleration:
$ma = \sum F$
$a = \frac{3.0~kN-1.0~kN}{m}$
$a = \frac{2000~N}{306~kg}$
$a = 6.5~m/s^2$
The acceleration of the sailplane is $6.5~m/s^2$ downward.
