Question

A rocket ship, with mass m=20,000kg, and engines mounted perpendicularly in the x and y directions, fires both rockets simultaneously. The engine oriented in the x-direction fires for 3s and shuts off. The engine oriented in the y-direction fires for 7s and shuts off. The force from the engine in the x-direction is 50,000N and the force from the engine in the y-direction is 100,000N. Make a scatter plot of the y-position of each particle as a function of the x-position, showing the trajectory of the rocket. Use Excel to determine the following: i) While the engines are firing, what is the acceleration of the rocket in the x and y directions? ii) After 7s, what is the velocity of the rocket in the x and y directions? iii) After 7s, what is the speed of the rocket? iv) After 7s, how far has the rocket travelled in the x-direction? How far has it travelled in the y-direction?, After 10 s? v) After 7s, what is the displacement of the rocket? After 10 s? Is the displacement of the rocket the same as the distance travelled? Explain. vi) If the mass of the rocket is doubled, what happens to the displacement? Mass (kg) Fx (N) Fy (N) ax (m/s2) ay (m/s2) 20000 50000 100000 time (s) vx(m/s) vy(m/s) v(m/s) x(m) y(m) d (m) 0 0.5 1

Answer 1

Do you mean find the final velocity? I'll assume this is what you mean.
Was the initial velocity zero? I'll assume it was.
You can't talk about 'acceleration during the initial velocity' - it doesn't make sense.

F = ma, so a = F/m
In x-direction a_x = 50,000/40,000 = 1.25m/s^2. Where do you get 2.5 from???
In y-direction a_y = 100,000/40,000 = 2.5m/s^2. Where do you get 5 from???

If the rocket was at rest to start with, then:
v_x = a_x*t = 1.25*3 = 3.75m/s
v_y = a_y*t = 2.5*7 = 17.5m/s

If you want the resultant, then
v = sqrt(3.75^2 + 17.5^2) = 17.9m/s
theta = tan-1(17.5/3.75) = 78degrees (anticlockwise from x-axis)
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If you know about impulse (= force * time), this is neater, as impulse = change of momentum:
50,000 * 3 = 40,000.v_x gives v_x
100,000 * 7 = 40,000.v_y gives v_y
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In response to you additional detail, you should assume initial velocity (v_i) is zero unless told otherwise, or the problem is impossible. The question should say the rocket starts from rest.
Your formula therefore simplify to give

In the x-direction:
x=(1/2)*a_x*t^2
v_x = a_x*t

In the t-direction:
y=(1/2)*a_y*t^2
v_y = a_y*t

So for example in x-direction when t=0.5s
x = (1/2)*a_x*t^2 = (1/2)*3.75*(0.5)^2 = 0.469m
v_x = a_x*t = 3.75*0.5 = 1.88m/s
Repeat this process up to for t=3s. After that remember v_x is constant and the value of x increases uniformly as the rocket moves at steady x-speed.

In x-direction when t=0.5s
y =(1/2)*a_y*t^2 = (1/2)*1`7.5*0.5^2 = 2.19m
v_y = a_y*t = 7.5*0.5 = 3.75m/s
Repeat this process for up to t=7s. After that remember v_y is constant and the value of y increases uniformly as the rocket moves at steady y-speed.