Physics, 16.09.2019 23:30 markmlg122

Afootball kicker can give the ball an initial speed of 30 m/s. he is 45 m from the goalpost which has a crossbar 2.90 m high. what is the smallest angle of elevation that he can kick the football and score a field goal?

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Answer from: gilliancarter2202

∅=10.7°

Explanation:

In parabolic motion the position on the x-axis can be found like this.

$x=V_{0}.cos \theta.t$

Where we clear the time.

$t=\frac{x}{v_{0}cos\theta}=\frac{45}{30cos\theta}$

The position on the y-axis can be found as well.

$y=v_{0}sin\theta.t-\frac{1}{2}a.t^{2} =30sin\theta.t-\frac{1}{2}9.8t^{2}$

replacing time.

$2.90=30sin\theta(\frac{45}{30cos\theta})-4.9(\frac{45}{30cos\theta})^{2}$

$2.9=45tan\theta-11.025sec^{2}\theta=45tan\theta-11.025(1+tan^{2}\theta)$

$-11.025tan^{2}\theta+45tan\theta-8.125=0$

Now we use the quadratic equation to find the tangent of the angle.

$tan\theta=3.89\\ and\\ tan\theta=0.19$

Finally we use the arc tangent function to find the angle.

$\theta=75.6\\ and\\ \theta=10.7$

We choose the second angle because it adapts to the situation described, that is the minimum angle.

Answer from: Quest

it doesn't. it was imagined up in the middle ages.

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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Afootball kicker can give the ball an initial speed of 30 m/s. he is 45 m from the goalpost which ha...