On a spacecraft, two engines are turned on for 666 s at a moment when the velocity of the craft has x and y components of velocity V0x = 3485 m/s and V0y = 5690 m/s. While the engines are firing, the craft undergoes a displacement that has components of x = 4.48 * 10^6 m and y = 6.96 * 10^6 m. Find the x and y components of the craft's acceleration.

Question

On a spacecraft, two engines are turned on for 666 s at a moment when the velocity of the craft has x and y components of velocity V0x = 3485 m/s and V0y = 5690 m/s. While the engines are firing, the craft undergoes a displacement that has components of x = 4.48 * 10^6 m and y = 6.96 * 10^6 m. Find the x and y components of the craft's acceleration.

So far, I tried this:
Vx = Vox + AxT
so Ax = (Vx-Vox)/T

so... Ax = (4.48*10^6 m - 3485 m/s)/666
Ax = 6721.494

But it says this is incorrect. What am I doing wrong? Please help!

Answer 1

THANK YOU for showing your work. We keep trying to get more students to do that but almost no one ever does.

The problem with your treatment is that you are confusing displacement with velocity. You plug in a displacement number and call it Vx. Then you try to subtract a speed from a length dimension. That is not allowed in physics.

You also need to show dimensions along with your numerical answers.

X = (1/2)*Ax*T^2 = 4.48*10^6 m when T = 666 s
Ax = 2*4.48*10^6/(666)^2 = 20.2 m/s^2

Y = 2*6.96*10^6/(666)^2 = 31.4 m/s^2

Answer 2

It says that is also incorrect...????

Answer 3

YOU DIDN'T HELP THE POOR GIRL drwls. GET YOUR ACT TOGETHER.

Answer 4

To find the components of the spacecraft's acceleration, you need to use the kinematic equation for displacement along with the information given about the engines firing and the initial velocity.

First, let's calculate the average velocity of the craft during the engines' firing. The average velocity can be calculated using the displacement and the time it took for that displacement:

Average velocity, Vavg = displacement / time = (x + y) / (666 s) = (4.48 * 10^6 m + 6.96 * 10^6 m) / 666 s = 19219.22 m/s

Next, we can calculate the change in velocity during the engines' firing. This change in velocity is equal to the final velocity minus the initial velocity:

Change in velocity, ΔV = Vavg - V0 = 19219.22 m/s - (3485 m/s + 5690 m/s) = 10044.22 m/s

Finally, we can calculate the components of the acceleration using the change in velocity and the time:

Ax = ΔVx / T = ΔV * cos(θ) / T
Ay = ΔVy / T = ΔV * sin(θ) / T

where ΔVx and ΔVy are the changes in the x and y components of velocity, respectively, and θ is the angle between the initial velocity and the displacement.

To calculate the angle θ, we can use the trigonometric identities:

tan(θ) = ΔVy / ΔVx
θ = tan^(-1)(ΔVy / ΔVx)

Substituting the values:

θ = tan^(-1)((6.96 * 10^6 m) / (4.48 * 10^6 m)) = 57.76°

Now we can calculate the components of the acceleration:

Ax = ΔV * cos(θ) / T = 10044.22 m/s * cos(57.76°) / 666 s ≈ 3714.03 m/s^2
Ay = ΔV * sin(θ) / T = 10044.22 m/s * sin(57.76°) / 666 s ≈ 8284.11 m/s^2

So, the x and y components of the craft's acceleration are approximately 3714.03 m/s^2 and 8284.11 m/s^2, respectively.

Note: Please check if your calculations for the average velocity and change in velocity match with the given information, as there might be a mistake in the given values. Additionally, make sure to round your final answers appropriately based on the significant figures provided in the problem statement.