Physics, 30.10.2019 01:31 mirianplacencia27

Asteel projectile is shot horizontally at 20m/s from the top of a 40m tower. how long does it take to hit the ground? how far from the base of the tower does the projectile hit the ground

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Answer from: dasharia

1) 2.86 s

To find the time of flight, we have to analyze the vertical motion of the stone, which is a uniformly accelerated motion (free fall) with constant acceleration (acceleration of gravity).

The vertical displacement at time t is given by

$s=u t + \frac{1}{2}gt^2$

where , taking downward as positive direction

is the initial vertical velocity (which is zero, since the projectile is shot horizontally)

t is the time

g=9.8 m/s^2 is the acceleration of gravity

In this problem we have

s = 40 m (vertical displacement is the height of the tower)

Solving for t, we find the time of flight: of the projectile:

$s=\frac{1}{2}gt^2\\t=\sqrt{\frac{2s}{g}}=\sqrt{\frac{2(40)}{9.8}}=2.86 s$

So, the projectile takes 2.86 s to hit the ground.

2) 57.2 m

The horizontal motion of the projectile is a uniform motion: in fact there are no forces acting on the projectile along the horizontal direction, so the horizontal acceleration is zero, and so the horizontal velocity is constant.

The initial horizontal velocity of the projectile is

v_x = 20 m/s

Therefore, to find the horizontal distance covered by the projectile, we can just use the equation

d=v_x t

And substitute the time of flight, which is the time at which the projectile hits the ground:

t = 2.86 s

So, we get:

d=(20)(2.86)=57.2 m

Answer from: Quest

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

$p(t)=0.3t^2+6t+80$

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

$p(0)=0+0+80=80$

according to question, we have said that if the population has twice its initial population, then it becomes

$p(t)=2\times 80=160$

so, time taken to reach this above mentioned population is given by

$160=0.3t^2+6t+80\\\\160-80=0.3t^2+6t\\\\80=0.3t^2+6t\\\\0.3t^2+6t-80=0\\\\\text{using quadratic formula ,we get }\\\\t_{1,\: 2}=\frac{-60\pm \sqrt{60^2-4\cdot \: 3\cdot \: 800}}{2\cdot \: 3}\\\\t=-29.14\ and\ t=9.149$

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

Answer from: Quest

Texture and composition are different because they are not the same aspect. texture has to do with feel and so on, where as composition is the chemical makeup which you cant touch like you can texture.

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Asteel projectile is shot horizontally at 20m/s from the top of a 40m tower. how long does it take t...

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