Physics, 17.09.2019 22:10 DissTrack

Aplacekicker must kick a football from a point 36.0 m (about 40 yards) from the goal. half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. when kicked, the ball leaves the ground with a speed of 22.6 m/s at an angle of 47.0° to the horizontal. (a) by how much does the ball clear or fall short of clearing the crossbar? (enter a negative answer if it falls short.) m (b) does the ball approach the crossbar while still rising or while falling? rising falling

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Answer from: AmbitiousAndProud

(a). H = 8.83 m

(b). Rising

Explanation:

Given,

Initial velocity of the ball = u = 22.6 m/sHeight of the crossbar = h = 3.05 mDistance of the crossbar from the initial position of the ball = r = 36.0 mAngle of projection = $\theta\ =\ 47.0^o$ Initial horizontal velocity of the ball = $u_x\ =\ ucos\theta$ Initial vertical velocity of the ball = $u_y\ =\ usin\theta$

part (a)

In the horizontal direction,

Ball is moving with the constant initial velocity of u_x

Let 't' be the time of the ball to reach at the crossbar of distance r.

$\therefore r = u_xt\\\Rightarrow t\ =\ \dfrac{r}{u_x}\ =\ \dfrac{r}{ucos\theta}\\\Rightarrow t\ =\ \dfrac{36.0}{22.6\times cos47^o}\\\Rightarrow t\ =\ 2.33\ sec$

At time 't', let 'y' be the vertical displacement attained by the ball.

From the equation of kinematics,

$y\ =\ u_yt\ -\ \dfrac{1}{2}gt^2\\\Rightarrow y\ =\ usin\theta t\ -\ \dfrac{1}{2}gt^2\\\Rightarrow y\ =\ 22.6sin47^0\times 2.33\ -\ 0.5\times 9.81\times 2.33^2\\\Rightarrow y\ =\ 11.88\ m$

Total distance of the ball above the crossbar = H = y - h = 11.88 - 3.05 = 8.83 m

part (b)

At the maximum height, vertical velocity of the ball becomes zero,

Let h be the maximum height attained by the ball.

From the kinematics,

$\therefore (v_y)^2\ =\ (u_y)^2\ -\ 2gh\\\Rightarrow 2gh\ =\ (u_y)^2\\\Rightarrow h\ =\ \dfrac{(u_y)^2}{2g}\\\Rightarrow h\ =\ \dfrac{(22.6\times sin47^o)^2}{2\times 9.81}\\\Rightarrow h\ =\ 13.92\ m$

Maximum height attained by the ball with the given initial velocity is 13.92 m but at the crossbar it attains 11.88 m. Hence the ball will still rising approaching the crossbar.

Answer from: Quest

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

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Answer from: Quest

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Aplacekicker must kick a football from a point 36.0 m (about 40 yards) from the goal. half the crowd...

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