Question

On a spacecraft, two engines are turned on for 684 s at a moment when the velocity of the craft has x and y components of v0x 4370 m/s and v0y 6280 m/s. While the engines are firing, the craft undergoes a displacement that has components of x4.11 106 m and y6.07 106 m. Find the x and y components of the craft's acceleration.

Answer 1

As we know by the kinematics

`\delta x = v_x * t + (1)/(2) at^2`

`4.11106 = 4370* 684 + (1)/(2)a_x*684^2`

`4.11106 = 2989080 + 233928*a_x`

`a_x = -12.78 m/s^2`

Similarly for Y direction

`\delta y = v_y * t + (1)/(2) at^2`

`6.07106 = 6280* 684 + (1)/(2)a_y*684^2`

`6.07106 = 4295520 + 233928*a_y`

`a_y = -18.36 m/s^2`

Answer 2

X - Component of acceleration = 4.79 m/s²

Y - Component of acceleration = 7.59 m/s²

Step-by-step explanation:

We have equation of motion, s = ut + 0.5 at²

X component:-

Initial velocity, u = 4370 m/s

Time, t = 684 s

Displacement, s = 4.11 x 10⁶ m

Substituting,

s = ut + 0.5 at²

4.11 x 10⁶ = 4370 x 684 + 0.5 x a x 684²

a = 4.79 m/s²

X - Component of acceleration = 4.79 m/s²

Y component:-

Initial velocity, u = 6280 m/s

Time, t = 684 s

Displacement, s = 6.07 x 10⁶ m

Substituting,

s = ut + 0.5 at²

6.07 x 10⁶ = 6280 x 684 + 0.5 x a x 684²

a = 7.59 m/s²

Y - Component of acceleration = 7.59 m/s²