Answer:
The magnitude and direction of the resultant force are approximately 599.923 newtons and 36.405°.
Explanation:
First, we must calculate the resultant force (
), in newtons, by vectorial sum:
(1)
Second, we calculate the magnitude of the resultant force by Pythagorean Theorem:
![\|\vec F\| = \sqrt{(482.843\,N)^{2}+(356.048\,N)^{2}}](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20F%5C%7C%20%3D%20%5Csqrt%7B%28482.843%5C%2CN%29%5E%7B2%7D%2B%28356.048%5C%2CN%29%5E%7B2%7D%7D)
![\|\vec F\| \approx 599.923\,N](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20F%5C%7C%20%5Capprox%20599.923%5C%2CN)
Let suppose that direction of the resultant force is an standard angle. According to (1), the resultant force is set in the first quadrant:
![\theta = \tan^{-1}\left(\frac{356.048\,N}{482.843\,N} \right)](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Ctan%5E%7B-1%7D%5Cleft%28%5Cfrac%7B356.048%5C%2CN%7D%7B482.843%5C%2CN%7D%20%5Cright%29)
Where
is the direction of the resultant force, in sexagesimal degrees.
![\theta \approx 36.405^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%20%5Capprox%2036.405%5E%7B%5Ccirc%7D)
The magnitude and direction of the resultant force are approximately 599.923 newtons and 36.405°.
Answer:
The runner´s speed is 2.2 m/s after 1.3 s.
Explanation:
The acceleration is the variation of velocity over time. If the acceleration is constant, then:
dv/dt = a
Separating variables:
dv = a · dt
integrating from initial velocity (v0) to v and from t = 0 to t:
v - v0 = a · t
v = v0 + a · t
Then usign this equation, we can calcualte the speed at t = 1.3 s:
v = 0 m/s + 1.7 m/s² · 1.3 s
v = 2.2 m/s
The runner´s speed is 2.2 m/s after 1.3 s.
Answer:
a = d p / dt = 23 m / s², The direction is the direction of the force
Explanation:
Newton's second law can be written in the form
F = dp / dt
How the body is initially at rest
F = m a
a = F /m
a = 6 /0.260
a = 23 m / s²
a = d p / dt = 23 m / s²
The direction is the direction of the force
There's some missing context here, but I would guess you're talking about a box or something with some mass <em>m</em> being pushed over a flat surface. Since it's moving with constant velocity, there is no acceleration and so the box is in equilibrium. In particular, the horizontal forces cancel each other. If <em>f</em> is the magnitude of the friction force, then
17 N + (-<em>f </em>) = 0
<em>f</em> = 17 N
and this force points opposite the direction of motion.