starting at rest on frictionless ice, a 50 kg person applies a constant 150 Newton force on a 75 kg person. The duration of the push is .15 seconds. At what speed does each of them end up moving?
To determine the final speed of each person, we need to apply Newton's second law of motion, which states that the acceleration of an object is equal to the net force applied on it divided by its mass:
a = F/m
Where:
a = acceleration
F = net force
m = mass
Let's calculate the acceleration of each person using the given values:
For the first person:
Mass (m1) = 50 kg
Net force (F1) = 150 N
a1 = F1 / m1
For the second person:
Mass (m2) = 75 kg
Net force (F2) = -150 N (since this force is applied in the opposite direction)
a2 = F2 / m2
Now that we have the acceleration for each person, we can calculate the final velocity using the equations of motion. Since both persons start at rest (initial velocity, u = 0), we will use the equation:
v = u + at
Where:
v = final velocity
u = initial velocity (0 in this case)
a = acceleration
t = time
For the first person:
v1 = 0 + a1 * t
For the second person:
v2 = 0 + a2 * t
Now, we can substitute the calculated values for a1, a2, and t:
v1 = a1 * t
v2 = a2 * t
Substituting the values, we get:
v1 = (F1 / m1) * t
v2 = (F2 / m2) * t
Let's plug in the values:
v1 = (150 N) / (50 kg) * 0.15 s
v2 = (-150 N) / (75 kg) * 0.15 s
Solving the equations will give us the final velocities of each person:
v1 = 4.5 m/s (rounded to one decimal place)
v2 = -3.0 m/s (rounded to one decimal place)
Therefore, the first person ends up moving in the positive direction with a final speed of 4.5 m/s, while the second person moves in the negative direction with a final speed of 3.0 m/s.