Question on Newton's Second Law of Motion

[Nivlac2425]

Homework Statement

A space probe has two engines. Each generates the same amount of force when fired, and the directions of these forces can be independently adjusted. When the engines are fired simultaneously and each applies its force in the same direction, the probe, starting from rest, takes 28 seconds to travel a certain distance. How long does it take to travel the same distance , again starting from rest, if the engines are fired simultaneously and the forces that they apply to the probe are perpendicular?

Homework Equations

F = ma
d = Vt + 1/2at^2

The Attempt at a Solution

I understand most of the question, but I am puzzled at how to find the acceleration when the two forces are perpendicular. I tried using the above equations, but I don't know exactly how to put everything together.
Thanks

 

[Perillux]

When you find the acceleration of the rocket divide it by 2 to find the acceleration applied by each engine.

If they are both perpendicular then they each make a 45 degree angle from their original positions.
So their horizontal components will cancel out, don't bother finding those. and just find the vertical component of 1 of them and multiply by 2 to find the acceleration of the rocket.
once you know that it should be easy to find the time.

 

[baba89]

for any help!

To find the acceleration when the two forces are perpendicular, we can use vector addition. Since the two forces are perpendicular, we can use the Pythagorean theorem to find the total force acting on the probe. Once we have the total force, we can use the equation F=ma to solve for the acceleration.

First, we can label the two forces as F1 and F2, with F1 being the force from the first engine and F2 being the force from the second engine. Since both engines generate the same amount of force, we can say that F1=F2.

When the two forces are applied in the same direction, the total force acting on the probe is simply the sum of the two forces, which we can represent as F1+F2.

However, when the two forces are perpendicular, we cannot simply add them together. Instead, we need to use vector addition to find the magnitude of the total force. This can be done by using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the two forces F1 and F2 form the legs of a right triangle, with the total force acting as the hypotenuse. So, we can use the equation F^2 = F1^2 + F2^2 to find the magnitude of the total force.

Once we have the total force, we can use the equation F=ma to solve for the acceleration. Then, we can use the equation d=Vt+1/2at^2 to find the time it takes for the probe to travel the same distance, starting from rest.

I hope this helps! Let me know if you need any further clarification.