Question

On a spacecraft, two engines are turned on for 794 s at a moment when the velocity of the craft has x and y components of v_0x = 2030 m/s and v_0y = 4430 m/s. While the engines are firing, the craft undergoes a displacement that has components of x = 4.05 x 10⁶ m and y = 4.13 x 10⁶ m. Find the (a) x and (b) y components of the craft's acceleration.

Answer 1

(a) for x component of acceleration of spacecraft,

given data :

initial velocity,v0x = 2030 m/s

time,t = 794 s

displacement,Sx = 4.05 * 10^6 m

using second equation of motion,

Sx = v0x * t + (1/2)*ax*t²

where ax is the x component of acceleration,

using the given data,

4.05 * 10^6 = 2030*794 + (0.5)*ax*794²

solving for ax

ax = 7.74 m/s²

thus the x component of acceleration is 7.74m/s².

(b) for y component of acceleration of spacecraft,

given data :

initial velocity,v0y = 4430 m/s

time,t = 794 s

displacement,Sy = 4.13 * 10^6 m

using second equation of motion,

Sy = v0y * t + (1/2)*ay*t²

where ay is the y component of acceleration,

using the given data,

4.13 * 10^6 = 4430*794 + (0.5)*ay*794²

solving for ay

ay = 1.95 m/s²

thus the y component of acceleration is 1.95m/s².