To find the distance from the origin after 4 seconds, we need to calculate the displacement of the body in both the x and y directions.
First, let's calculate the displacement in the x-direction. We can use the equation of motion:
x = ut + (1/2)at^2
where:
x - displacement in the x-direction
u - initial velocity in the x-direction
t - time
a - acceleration in the x-direction
Given:
u = 5 m/s (initial velocity in the x-direction)
t = 4 s (time)
Since this is a gravity-free space and there are no external forces acting on the body in the x-direction, the acceleration in the x-direction is zero (a = 0). Therefore, the displacement in the x-direction can be calculated as:
x = u * t = 5 m/s * 4 s = 20 m
Next, let's calculate the displacement in the y-direction. The body is subjected to a constant force of 4 N in the y-direction. We can use Newton's second law of motion:
F = ma
where:
F - force
m - mass
a - acceleration
Given:
F = 4 N (force in the y-direction)
m = 2 kg (mass)
Since the body is in a gravity-free space, there is no gravitational force acting on it. Therefore, the only force acting on the body is the 4 N force in the y-direction. Using Newton's second law, we can solve for the acceleration:
a = F / m = 4 N / 2 kg = 2 m/s^2
Now, we can calculate the displacement in the y-direction using the equation of motion:
y = ut + (1/2)at^2
where:
y - displacement in the y-direction
u - initial velocity in the y-direction (which is zero in this case since the body is not given an initial velocity in the y-direction)
t - time
a - acceleration in the y-direction
Given:
u = 0 m/s (initial velocity in the y-direction)
t = 4 s (time)
a = 2 m/s^2 (acceleration in the y-direction)
Plugging in the values, the displacement in the y-direction can be calculated as:
y = (1/2)at^2 = (1/2) * 2 m/s^2 * (4 s)^2 = 16 m
Finally, we can find the distance from the origin after 4 seconds using the Pythagorean theorem:
distance = sqrt(x^2 + y^2)
= sqrt(20 m^2 + 16 m^2)
= sqrt(400 m^2 + 256 m^2)
= sqrt(656 m^2)
โ 25.61 m
Therefore, the distance from the origin after 4 seconds is approximately 25.61 meters.