On a spacecraft, two engines are turned on for 789 s at a moment when the velocity of the craft has x and y components of v0x = 5410 m/s and v0y = 8100 m/s. While the engines are firing, the craft undergoes a displacement that has components of x = 2.78 x 106 m and y = 4.73 x 10^6m. Find the (a) x and (b) y components of the craft's acceleration.

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nuuk nuuk · Answer 1 · 2019-10-18T10:08:44+02:00

Answer:

Explanation:

Given

time for which spacecraft turned on is 789 s

[tex]v_{0x}=5410 m/s[/tex]

[tex]v_{0y}=8100 m/s[/tex]

[tex]x=2.78\times 10^6 m[/tex]

[tex]y=4.73\times 10^6 m[/tex]

we know [tex]s=ut+\frac{at^2}{2}[/tex]

[tex]2.78\times 10^6=5410\times 789+\frac{a_x(789)^2}{2}[/tex]

[tex]2.78=4.268+a_x\times 0.622[/tex]

[tex]a_x=-2.392 m/s^2[/tex]

For y component

[tex]s=ut+\frac{at^2}{2}[/tex]

[tex]4.73\times 10^6=8100\times 789+\frac{a_y(789)^2}{2}[/tex]

[tex]4.73=6.39+a_y\times 0.622[/tex]

[tex]a_y=-2.66 m/s^2[/tex]