4.

A jet makes a landing traveling due east with a speed of 120 m/s .

vesna_86 [32]

Average acceleration over a time interval lasting $\Delta t$ is

$a_{\rm ave}=\dfrac{\Delta v}{\Delta t}$

where $\Delta v$ is the difference in the jet's final and initial velocities. It's coming to a rest, so

$a_{\rm ave}=\dfrac{0-120\frac{\rm m}{\rm s}}{13.5\,\rm s}=-8.9\dfrac{\rm m}{\mathrm s^2}$

so the average acceleration has magnitude 8.9 m/s^2 and is pointing West (the direction opposite the jet's movement, which should make sense because the jet is slowing down).

7 0

4 years ago

A chimpanzee sitting against his favorite tree gets up and walks 70.9 m due east and 31.9 m due south to reach a termite mound,

DIA [1.3K]

A right triangle is formed by the 70.9 m walked east and 31.9 m walked south.
The legs of this right triangle are 70.9 and 31.9.
The shortest distance between two points is a straaight line. Therefore the hypotenuse of this triangle is going to be that shortest distance.
We can use the Pythagorean Theorem to find the hypotenuse of this triangle.
$a^2+b^2=c^2\\70.9^2+31.9^2=c^2\\5026.81+1017.61=c^2\\6044.42=c^2\\c=\sqrt{6044.42}$

$c=\sqrt{6044.42}\approx\boxed{77.7458681}\ (decimal\ form)\\\\c=\sqrt{6044.42}=\sqrt{\frac{604442}{100}}=\boxed{\frac{\sqrt{604442}}{10}}\ (exact\ form)$

As for the second part of the question, we want to find the angle formed by the hypotenuse and the 31.9 walked east.
We could use any of the three trigonometric ratios here since we know all 3 sides.
sine = opposite / hypotenuse
cosine = adjacent / hypotenuse
tangent = opposite / adjacent
I am going to use tangent, because then I won't have to deal with the hypotenuse and so the answer will be more accurate.

If you haven't already drawn yourself a diagram, now is a good time to.
The side opposite our angle is the 31.9, and the adjacent is 70.9.
Therefore, $\tan(m\angle)=\frac{31.9}{70.9}$ .

We can use inverse trig ratios here to find the measure of our angle.
$\tan^{-1}(\tan(m\angle))=\tan^{-1}(\frac{31.9}{70.9})\\\\m\angle=\tan^{-1}(\frac{31.9}{70.9})\approx\boxed{24.2243851\°\ or\ 0.422795279\ rad}$

4 0

3 years ago

The distance between the centers of the wheels of a motorcycle is 146 cm. The center of mass ofthe motorcycle, including the rid

Vitek1552 [10]

Answer:

9.12267515924 m/s²

Explanation:

Here the moment created by the wheels and the moment created by the center of gravity will balance each other.

h = Height of the center of mass = 78.5 cm

d = Distance from back wheel to the center of mass = $\dfrac{146\times 10^{-2}}{2}\ m$

g = Acceleration due to gravity = 9.81 m/s²

a = Horizontal acceleration

The equation is of the form

$mgd=Fh\\\Rightarrow mgd=mah\\\Rightarrow a=\dfrac{gd}{h}\\\Rightarrow a=\dfrac{9.81\times \dfrac{146\times 10^{-2}}{2}}{78.5\times 10^{-2}}\\\Rightarrow a=9.12267515924\ m/s^2$

The horizontal acceleration of the motorcycle that will make the front wheel rise off the ground is 9.12267515924 m/s²

8 0

3 years ago

Where did beowulf and his warriors take the skull

dedylja [7]

I'm pretty sure Beowulf took the skull to Herot.

6 0

3 years ago

How much energy is required to move 2 electrons through a potential difference of 1.0 x 10^ 2 volts?

Ksenya-84 [330]

Charge of electron = 1.6×10−¹⁹

(1.6×10−¹⁹)(1×10²) (2e)

= 3.2×10−¹⁷ J

3 0

3 years ago