"The condition of equilibrium is when the sum of the forces acting on a body is the zero vector. Suppose a body has a force of 2 pounds acting on it to the right, 5 pounds acting on it upward, and 3 pounds acting on it 45° from the horizontal. What single force is needed to produce a state of equilibrium on the body?"

The answer is pounds

Explanation:

We will start this question by representing the force vectors in Cartesian coordinate system:

Let the single force we need be represented by

Since, the body is in equilibrium the summation of all the forces acting on it should be zero:

∑ (Sum of all forces in direction is equal to zero)

( component of force 3 is negative because it is acting  in opposite direction)

∑ (Sum of all forces in direction is equal to zero)

( component of force 3 is negative because it is acting  in opposite direction)

So,

Hence, to get the scalar quantity of a single force:

pounds

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s

snell's law

refractve index = sin incidence / sin refraction