A soccer ball was kicked off a cliff that was h = 8.4 m above the ground. The ball was kicked at a speed of 25 m s-1 and an angle of 20 to the horizon.
What is magnitude of the horizontal displacement of the ball? Use g = 9.8 m s-2.
proper equation and help plz
Vo = 25m/s[20o].
Xo = 25*Cos20 = 23.5 m/s.
Yo = 25*sin20 = 8.55 m/s.
Y = Yo + g*Tr = 0.
8.55 - 9.8Tr = 0, Tr = 0.873 s. = Rise time.
Y^2 = Yo^2 + 2g*h = 0.
(8.55)^2 - 19.6h = 0, h = 3.73 m. Above the cliff.
0.5g*Tf^2 = 3.73+8.4
4.9Tf^2 = 12.13, Tf = 1.57 = Fall time.
Dx = Xo(Tr+Tf) = Hor. disp.
To determine the magnitude of the horizontal displacement of the ball, we need to use the equation of motion that relates the horizontal displacement, vertical displacement, initial velocity, launch angle, and gravity.
The equation we will use is:
Horizontal displacement = (initial velocity * time) * cos(angle)
First, we need to find the time it takes for the ball to hit the ground. We can do this by calculating the vertical displacement.
Initial vertical velocity = initial velocity * sin(angle)
Using the equation of motion for vertical displacement:
Vertical displacement = (initial vertical velocity * time) - (0.5 * acceleration * time^2)
Since the ball starts at a height of 8.4 m and ends at a height of 0 m:
0 = (initial vertical velocity * time) - (0.5 * acceleration * time^2)
Simplifying the equation, we get:
0.5 * acceleration * time^2 = (initial vertical velocity * time)
Solving for time:
time = (initial vertical velocity) / acceleration
Now, we can calculate the initial vertical velocity:
Initial vertical velocity = initial velocity * sin(angle)
Substituting the given values:
Initial vertical velocity = 25 m/s * sin(20°)
Now we can substitute the values into the equation to find the time:
time = (initial vertical velocity) / acceleration
time = (25 m/s * sin(20°)) / 9.8 m/s^2
Once we have the time, we can calculate the horizontal displacement using the equation:
Horizontal displacement = (initial velocity * time) * cos(angle)
Substituting the given values:
Horizontal displacement = (25 m/s * time) * cos(20°)
Finally, we can calculate the magnitude of the horizontal displacement by taking the absolute value of the result:
Magnitude of horizontal displacement = |Horizontal displacement|
Remember to use the proper order of operations, convert angles to radians if required, and round the final answer to an appropriate number of significant figures.