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

Answer:

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

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

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=$4.5\times 10^6 m$

y component of displacement of craft=$7.27\times 10^6 m$

We know that velocity=$\frac{displacement}{time}$

x component of final velocity of craft= $\frac{4.5\times 10^6}{763}=5897.78 m/s$

y component of final velocity of craft=$\frac{7.27\times 10^6}{763}=9528.18 m/s$

We know that acceleration =$\frac{v-u}{t}$

a.x component of acceleration of craft=$\frac{5897.78-6380}{763}=-0.63 m/s^2$

b.y component of acceleration of craft=$\frac{9528.18-6770}{763}=3.61 m/s^2$

Answer 2

Answer:

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 $x=4.50\times 10^6$

$y=7.27\times 10^6$

Using $s=ut+\frac{at^2}{2}$ in x and y direction

$x=v_0_x\times t+\frac{at^2}{2}$

$4.50\times 10^6=6380\times 763+\frac{a\times 763^2}{2}$

$4.50\times 10^6-4.86\times 10^6=\frac{a\times 763^2}{2}$

$a=-1.23 m/s^2$

In y direction

$y=v_0_y\times t+\frac{a't^2}{2}$

$7.27\times 10^6=6770\times 763+\frac{a\times 763^2}{2}$

$7.27\times 10^6-5.16\times 10^6=\frac{a\times 763^2}{2}$

$a=7.24 m/s^2$

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

y component$=7.24 m/s^2$