Physics, 12.07.2019 03:30 glawson2

Aslingshot launches a stone vertically with an initial velocity of 400 ft/s from an initial height of 10 ft. find the average velocity over time interval [3, 8]. (assume g = 32 ft/s2) ft/s

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Answer from: 902coo

576 ft/s The distance the stone will have traveled is expressed by the formula d = VT + 0.5AT^2 where d = distance V = initial velocity T = time A = acceleration Since the stone is given an initial velocity of 400 ft/s, it will take 400/32 = 12.7 seconds for it to stop and start falling to the ground, which is comfortably larger than the upper time value for the interval [3,8]. So let's see how far the stone has traveled at T=3 and T=8 d = VT + 0.5AT^2 d = 400T + 16T^2 d = 400*3 + 16*3^2 = 1200 + 16*9 = 1200 + 144 = 1344 d = 400*8 + 16*8^2 = 3200 + 16*64 = 3200 + 1024 = 4224 So the stone traveled a distance of 4224-1344 = 2880 feet during the specified interval. And since the interval spanned 8-3 = 5 seconds, the average velocity will be 2880/5 = 576 ft/s

Answer from: jayyd679

We want to study the vertical motion of a stone, to do it, we will find the motion equations of the stone.

We will find that the average velocity in the given interval is 224 ft/s.

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First, we need to find the acceleration of the stone.

The only force acting on the stone (ignoring air resistance) will be the gravitational force, then the acceleration of the stone will be equal to the gravitational acceleration.

a(t) = -32ft/s^2

To get the velocity equation we need to integrate over time, such that the constant of integration will be equal to the initial velocity, which we know is equal to 400ft/s

Then we get:

v(t) = (-32 ft/s^2)*t + 400ft/s

To get the position equation we integrate again, this time the constant of integration will be the initial position, 10 ft.

p(t) = (-16ft/s^2)*t^2 + (400ft/s)*t + 10ft

Now the average velocity is defined as the quotient between the displacement and the time it took to do that displacement, then the average velocity will be:

$av = \frac{p(8s) - p(3s)}{8s - 3s} \\\\av = \frac{( (-16ft/s^2)*(8s)^2 + (400ft/s)*8s + 10ft) - ((-16ft/s^2)*(3s)^2 + (400ft/s)*3s + 10ft)}{5s} = 224 ft/s$

Thus the average velocity in that interval is 224 ft/s

If you want to learn more, you can read:

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Answer from: Quest

to be honest as much as i would love to answer this. i feel as if something's missing. just saying.

Answer from: Quest

co2reflects heat radiation back to earth buning coal and oil emits co2 globe warms

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