You performed an experiment to find out how strong the net below a trapeze should be to safely catch a performer of mass 80 kg.
2 answers:
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Answer:
Newton's second law
Explanation:
Mathematically, Newton's second law can be written as
where
F is the net force on the particle
m is its mass
a is the acceleration
This can also be rewritten as
which means that the acceleration is directly proportional to the force and inversely proportional to the mass. If the net force is non-zero, it means that the particle has a non-zero acceleration, therefore its velocity is changing (it can be changing either in magnitude, if the force has same direction as the velocity, or also in direction, if the force has a different direction).
The horizontal distance traveled by the ball (range of motion) is given by the following equation:
In which
is the range of motion, 
is the horizontal component of the initial velocity, and 
is the time of motion.
First, lets calculate the horizontal component of the initial velocity:
Now, we calculate the time of motion from the equation that described the motion of the ball in the vertical axis:
In which
is the position of the ball vertically, 
is the vertical component of the initial velocity, 
is the acceleration in the vertical axis (which is gravity), and is time of motion.
We want to find the time when the ball lands, hence, when
; so the equation becomes:
We rewrite it a bit more:
This is a quadratic equation, so we use the quadratic equation formula to solve for time (we'll get two answers):
![t= -\frac{1}{9.8} [{-7.97}+-\sqrt{(7.97)^2}]](https://tex.z-dn.net/?f=t%3D%20%20-%5Cfrac%7B1%7D%7B9.8%7D%20%5B%7B-7.97%7D%2B-%5Csqrt%7B%287.97%29%5E2%7D%5D)
Clearly, one of the answers is
, this is before you kick the ball (it is on the ground), we want the nonzero answer (when it lands) so:
Now, we plug-in the time value to the equation of the motion's range:
The ball will travel 18.57 meters.
In which
First, lets calculate the horizontal component of the initial velocity:
Now, we calculate the time of motion from the equation that described the motion of the ball in the vertical axis:
In which
We want to find the time when the ball lands, hence, when
We rewrite it a bit more:
This is a quadratic equation, so we use the quadratic equation formula to solve for time (we'll get two answers):
Clearly, one of the answers is
Now, we plug-in the time value to the equation of the motion's range:
The ball will travel 18.57 meters.