Distance is the length of a path followed by a particle. The displacement of a particle is defined as its change in position in
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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.
Answer:
0.176 m/s
Explanation:
given,
mass of the puck, m = 170 g
Length of the ramp, L = 3.6 mm
angle of inclination, θ = 26°
the minimum speed require to reach at the top of the ramp
using equation of motion
v² = u² + 2 a s
final speed of the puck is zero
0² = u² - 2 g s
height of the pluck
h = 1.58 mm
h = 0.00158 m
now,
u = 0.176 m/s
hence, the speed required by the pluck to reach at the top is equal to 0.176 m/s