Question

1. a 1000 kg satellite in space needs a course correction. to achieve this, one of its rocket motors is fired to apply 100 n of force as thrust. the rocket boosters then fire in the opposite direction to realign the satellite with a force of 25 n. what will be the acceleration due to this thrust?
2. a tiny aeroplane accelerates at 35 m/s² with a force of 20 n. wind resistance blows against the plane with a force of 4n. what is the mass of the aeroplane?
3. a bow hunter fires an arrow with a force of 500 n and a mass of 27.3 kg. the wind towards the arrow with a force of 25 n making it slow down find the net force and calculate the acceleration.
4. a person is riding a bike and accelerating at 2.8 m/s² with a force of 100 n. the friction from the sidewalk is acting with a force of 17n. what is the mass of the rider and bicycle?
5. a 35 kg child jumps on a trampoline on the moon and becomes airborne. they hit the trampoline safely with a force of 20 n. gravity is pushing the child down on the trampoline with a force of 12n.what was their downward acceleration?

Explanation:

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Step1: Calculate net - force

The main thrust is 100 N and the opposing force is 25 N. The net - force $F_{net}$ is the difference between the two forces.
$F_{net}=100 - 25=75$ N

Step2: Use Newton's second law

Newton's second law is $F = ma$, where $F$ is the net - force, $m$ is the mass, and $a$ is the acceleration. We know $F_{net}=75$ N and $m = 1000$ kg. Solving for $a$, we get $a=\frac{F_{net}}{m}$.
$a=\frac{75}{1000}=0.075$ m/s²

Step1: Calculate net - force

The force applied to the aeroplane is $F = 20$ N and the wind resistance is $F_{r}=4$ N. The net - force $F_{net}$ is $F_{net}=20 - 4 = 16$ N.

Step2: Use Newton's second law

Newton's second law is $F = ma$, where $F$ is the net - force, $m$ is the mass, and $a$ is the acceleration. We know $F_{net}=16$ N and $a = 35$ m/s². Solving for $m$, we get $m=\frac{F_{net}}{a}$.
$m=\frac{16}{35}\approx0.46$ kg

Step1: Calculate net - force

The force applied to the arrow is $F = 500$ N and the wind force is $F_{w}=25$ N. The net - force $F_{net}$ is $F_{net}=500 - 25=475$ N.

Step2: Calculate acceleration

Using Newton's second law $F = ma$, where $m = 27.3$ kg and $F_{net}=475$ N. Solving for $a$, we get $a=\frac{F_{net}}{m}$.
$a=\frac{475}{27.3}\approx17.4$ m/s²

Answer:

$0.075$ m/s²

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