Physics, 28.02.2020 03:56 322251

A rocket is fired from rest at x = 0 and travels along a parabolic trajectory described by y 2 = [120(10 3 )x] m. If the x component of acceleration is a x = ( 4 1 t 2 ) , m/s 2 , where t is in seconds, determine the magnitude of the rockets velocity and acceleration when t = 10 s.

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Answer from: jessicaisbaehood

The velocity is 1003.5 m/s and the acceleration is 103.1 m/ $s^{2}$ .

Explanation:

We need to find the parameter equation of x. To find it, we will need to integrate the x-component acceleration equation given to us, twice. Acceleration is:

a = $\frac{dv}{dt}$

dv = adt

∫dv = ∫adt

$\int\limits^v_0 \, dv$ = $\int\limits^t_0 {\frac{1}{4}t^{2} } \, dt$

v = $\frac{1}{12} t^{3} m/s$ .

Velocity is:

v = $\frac{dx}{dt}$

dx=vdt

Again, integrate both sides:

∫dx = ∫vdt

$\int\limits^x_0 dx$ = $\int\limits^t_0 {\frac{1}{12} t^{3} } \, dt$

x = $\frac{1}{48} t^{4} m$

Substitute our x equation into our parameter equation of y.

y $^{2}$ = [120( $10^{3}$ )x] m

y $^{2}$ = [120( $10^{3}$ )( $\frac{1}{48}$ )( $t^{4}$ ) ]

(take the square root of both sides and simplify)

y = 50 $t^{2}$

Now that we can represent our equation with respect to time, we can take the derivative to figure out the velocity. Remember that taking the derivative of a position function gives us the velocity function.

y = 50 $t^{2}$

vy= y = 100t

Let us write down the two equations for velocity we found:

vx = $\frac{1}{12} t^{3} m/s$

vy = 100t m/s

At t = 10 s:

vx = $\frac{1}{12} 10^{3}$ = 83.3 m/s

vy = 100(10)=1000 m/s

The magnitude of velocity is:

v = $\sqrt{(vx)^{2}+(vy)^{2} }$

v = $\sqrt{(83.3)^{2}+(1000)^{2} } = 1003.5 m/s$

To figure out the acceleration, we need to figure out ay which can be found by taking the derivative of the vy equation,

vy = 100t m/s

ay = vy = 100 m/ $s^{2}$

Since ax is given to us in the question, we have the following:

ax = $(\frac{1}{4}t^{2}) m/s^{2}$

ay = 100 m/ $s^{2}$

At t = 10 s:

ax = $(\frac{1}{4}10^{2})} =25 m/s^{2$

ay = 100 m/ $s^{2}$

The magnitude of acceleration is equal to:

a = $\sqrt{(ax)^{2}+(ay)^{2} }$

a = $\sqrt{(25)^{2}+(100)^{2} }$

a= 103.1 m/ $s^{2}$

Final Answers:

v = 1003.5 m/s

a= 103.1 m/ $s^{2}$

Answer from: Quest

volts times amps 6 x 0.5 3w

Answer from: Quest

answer;

d. are made mostly of liquid

explanation;

-the general composition and structure planets includes; they have a thick gas and liquid layer covering a small,solid core. mostly the gases are hydrogen and helium atmosphere and layers of liquid hydrogen. for instance neptune and uranus are examples of the outer planets, they have a core covered by ice and ammonia.

-neptune's atmosphere is hydrogen and helium with a bit of methane so there is no oxygen to breath and the interior is made up of frozen water and ammonia with a rock and iron core. thus, there is no liquid water or solid surface to survive.

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A rocket is fired from rest at x = 0 and travels along a parabolic trajectory described by y 2 = [12...

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