A soccer ball is kicked upward from the ground with an initial vertical velocity of 3.6 meters per second. After how many seconds does it land?
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The total time in the air (T), if kicked straight up at initial velocity Vo, is twice the time that it takes to reach zero velocity. Maximum height is reached at t = T/2
T = 2 Vo/g = 2*3.6/9.8 = 0.73 seconds
The same answer will apply if Vo is the initial vertical COMPONENT of velocity. That was probably the intent of the question.
I overloooked your question at first becasue I am not an expert on quails.
To find out how many seconds it takes for the soccer ball to land, we first need to determine the time it takes for the ball to reach its maximum height and then double that time to get the total time of the ball's flight.
The vertical motion of the ball can be described using the equations of motion:
h = vi * t + (1/2) * g * t^2
Where:
h = height (in this case, the ball's maximum height)
vi = initial vertical velocity (3.6 meters per second, going upwards)
g = acceleration due to gravity (approximately 9.8 meters per second squared, acting downward)
t = time
Since we want to find the time it takes for the ball to reach its maximum height, let's set the final height equal to zero (since it will land back on the ground), and solve the equation for time:
0 = 3.6 * t + (1/2) * 9.8 * t^2
Now, let's simplify and rearrange the equation:
4.9 * t^2 + 3.6 * t = 0
We can factor out t from the equation:
t(4.9 * t + 3.6) = 0
This equation will be zero when either t = 0 or 4.9 * t + 3.6 = 0.
Since time cannot be negative, we can disregard the first solution and focus on the second one:
4.9 * t + 3.6 = 0
Subtracting 3.6 from both sides:
4.9 * t = -3.6
Dividing by 4.9:
t = -3.6 / 4.9
t ≈ -0.735
It appears we have obtained a negative time, which is not meaningful in this context. This is because the squared term in the equation can result in two possible solutions. In this case, we consider the negative solution negligible since time cannot be negative.
So, the ball takes approximately 0.735 seconds to reach its maximum height.
To find the total time of flight, we double the time it took to reach the maximum height:
Total time of flight = 2 * 0.735
Total time of flight ≈ 1.47 seconds
Therefore, it takes approximately 1.47 seconds for the soccer ball to land back on the ground.