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3 years ago

R = 4 in., θ = 11 rad; find s

Mathematics

1 answer:

son4ous [18]3 years ago

4 0

Answer:

The arc length s = 44 inches

Step-by-step explanation:

We are given:

r = 4 in

Ф = 11 radians

We need to find s

The formula used is: $s=r\theta$

where s represents arc length, r is radius and Ф is angle in radians

Putting values and finding s

$s=r\theta$

Put r = 4 and Ф = 11

$s=4\times 11\\s=44$

So, the arc length s = 44 inches

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Jeff is standing on top of a tree next to a mysterious monolith (a big rectangular box). At time t = 0, Jeff threw a coconut ver

zimovet [89]

Answer:

$h=\frac{h_{m}-h_{t}+44.145}{3}t-4.905t^{2}+h_{t}$

(if the heights are measured in meters)

Step-by-step explanation:

In order to solve this problem we will need to first draw a diagram of the situation (see attached picture) and then, make use of the following physics equation:

$y_{f}=\frac{1}{2}at^{2}+v_{0}t+y_{0}$

where:

$y_{f}$ =height of the object at a given time t

a=acceleration due to gravity

t=time

$v_{0}$ =initial velocity of the object

$y_{0}$ =initial height of the object.

we know most of this data, except for the height of theh object at the given time t and the initial velocity of theh object. We can make use of the given time to write the velocity in terms of the height of thte tree and the height of the monolith.

So let's substitute the values we know so far:

$h=\frac{1}{2}(-9.81)t^{2}+v_{0}t+h_{tree}$

the problem tells us that after 3 seconds, the object reaches the height of the monolith, so let's do the substitution:

$h_{monolith}=\frac{1}{2}(-9.81)(3)^{2}+v_{0}(3)+h_{tree}$

we can now solve this equation for the initial velocity, so we get:

$h_{monolith}-h_{tree}=-44.145+3v_{0}$

$h_{monolith}-h_{tree}+44.145=3v_{0}$

so:

$v_{0}=\frac{h_{monolith}-h_{tree}+44.145}{3}$

and now we can substitute this back into the original formula to get the equation that represents the height of the coconut above the ground after t seconds:

$h=\frac{h_{m}-h_{t}+44.145}{3}t-4.905t^{2}+h_{t}$