Answer:
8.76762 m
Explanation:
T = Time period = 5.94 seconds
g = Acceleration due to gravity = 9.81 m/s²
L = Length of pendulum = Height of tower
Time period is given by

The height of the tower is 8.76762 m
For the ball to go straight into the goal, the kicker needs to be no more than 6.54 meters away from the goal.
For the ball to arc into the goal, the kicker needs to be between 58.5 and 65.1 meters away from the goal.
<h3>Explanation</h3>
How long does it take for the ball to reach the goal?
Let the distance between the kicker and the goal be
meters.
Horizontal velocity of the ball will always be
until it lands if there's no air resistance.
The ball will arrive at the goal in
seconds after it leaves the kicker.
What will be the height of the ball when it reaches the goal?
Consider the equation
.
For this soccer ball:
,
,
since the player kicks the ball "from ground level."
when the ball reaches the goal.
.
Solve this quadratic equation for
,
.
meters when
meters.
or
meters when
meters.
In other words,
- For the ball to go straight into the goal, the kicker needs to be no more than 6.54 meters away from the goal.
- For the ball to arc into the goal, the kicker needs to be between 58.5 and 65.1 meters away from the goal.
The ball only accelerates during the brief time that the club is in contact
with it. After it leaves the club face, it takes off at a constant speed.
If it accelerates at 20 m/s² during the hit, then
Force = (mass) x (acceleration) = (0.2kg) x (20 m/s²) = <em>4 newtons</em> .
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