Question

two engines are turned on for 763 s at a moment when the velocity of the craft has x and y components of v0x = 6380 m/s and v0y = 6770 m/s. While the engines are firing, the craft undergoes a displacement that has components of x = 4.50 x 106 m and y = 7.27 x 106 m. Find the (a) x and (b) y components of the craft's acceleration.

Answer 1

a.x component of acceleration of craft=
`-0.63 m/s^2`

b.y component of acceleration of craft=
`3.61 m/s^2`

Step-by-step explanation:

We are given that two engines are turned on for 763 s.

x component of initial velocity of craft=
`v_x_0=6380 m/s`

y component of initial velocity of craft=
`v_y_0=6770 m/s`

After firing,

x component of displacement of craft=
`4.5* 10^6 m`

y component of displacement of craft=
`7.27* 10^6 m`

We know that velocity=
`(displacement)/(time)`

x component of final velocity of craft=
`(4.5* 10^6)/(763)=5897.78 m/s`

y component of final velocity of craft=
`(7.27* 10^6)/(763)=9528.18 m/s`

We know that acceleration =
`(v-u)/(t)`

a.x component of acceleration of craft=
`(5897.78-6380)/(763)=-0.63 m/s^2`

b.y component of acceleration of craft=
`(9528.18-6770)/(763)=3.61 m/s^2`

Answer 2

Step-by-step explanation:

Given

initial velocity component of engines is

`v_0_x=6380 m/s`

`v_0_y=6770 m/s`

time period of engine running=763 s

Displacement in
`x=4.50* 10^6`

`y=7.27* 10^6`

Using
`s=ut+(at^2)/(2)` in x and y direction

`x=v_0_x* t+(at^2)/(2)`

`4.50* 10^6=6380* 763+(a* 763^2)/(2)`

`4.50* 10^6-4.86* 10^6=(a* 763^2)/(2)`

`a=-1.23 m/s^2`

In y direction

`y=v_0_y* t+(a't^2)/(2)`

`7.27* 10^6=6770* 763+(a* 763^2)/(2)`

`7.27* 10^6-5.16* 10^6=(a* 763^2)/(2)`

`a=7.24 m/s^2`

x component
`=-1.23 m/s^2`

y component
`=7.24 m/s^2`