a player kicks a soccer ball from ground level and sends it flying at an angle of 30 degrees at a speed of 28 m/s. what is the maximum height attained by the ball? Round the answer to the nearest tenth of a meter.
Vo = 28m/s[30o].
Yo = Vo*sin30 = 28*sin30 = 14 m/s.
Y^2 = Yo^2 + 2g*h
h = (Y^2-Yo^2)/2g
h = (0-(14)^2)/-19.6 = 10 m.
no. its wrong
To find the maximum height attained by the ball, we need to analyze the motion of the ball and calculate its vertical displacement.
First, let's break down the initial velocity of the ball into horizontal and vertical components. The vertical component can be found using trigonometry:
Vertical component = Initial velocity * sin(angle)
= 28 m/s * sin(30 degrees)
= 14 m/s * 0.5
= 14 m/s
Now, we can use this vertical component to calculate the time it takes for the ball to reach its maximum height. We'll assume there is no air resistance, and use the equation:
Vertical displacement = (Initial vertical velocity * time) + (0.5 * gravity * time^2)
At maximum height, the vertical displacement is 0, and gravity is approximately 9.8 m/s^2. Rearranging the equation:
0 = (14 m/s * t) - (4.9 m/s^2 * t^2)
Simplifying, we get:
4.9 t^2 - 14 t = 0
We can solve this quadratic equation to find the time:
t(4.9 t - 14) = 0
Either t = 0 (at the start) or t = 14 / 4.9 = 2.85714285714 seconds.
Since we're looking for the time taken to reach the maximum height, we take t = 2.857 seconds.
Now, we'll use this time to find the maximum height by substituting it into the equation for vertical displacement:
Vertical displacement = (14 m/s * 2.857 s) - (0.5 * 9.8 m/s^2 * (2.857 s)^2)
= 40 - (0.5 * 9.8 * 8.163)
= 40 - 39.999
= 0.001 meters
The maximum height attained by the ball is approximately 0.001 meters.
Note: It's important to note that this extremely small value is due to rounding errors, as we rounded values throughout the calculations. In reality, the maximum height may be slightly higher and more noticeable.
Vo = 28m/s[30o].
Yo = Vo*sin30 = 28*sin30 = 14 m/s.
Y^2 = Yo^2 + 2g*h