Answer:
(a)
, (b)
, (c) ![W = -51](https://tex.z-dn.net/?f=W%20%3D%20-51)
Explanation:
The statement is incomplete:
The force on an object is
. For the vector
. Find: (a) The component of
parallel to
, (b) The component of
perpendicular to
, and (c) The work
, done by force
through displacement
.
(a) The component of
parallel to
is determined by the following expression:
![\vec F_{\parallel} = (\vec F \bullet \hat {v} )\cdot \hat{v}](https://tex.z-dn.net/?f=%5Cvec%20F_%7B%5Cparallel%7D%20%3D%20%28%5Cvec%20F%20%5Cbullet%20%5Chat%20%7Bv%7D%20%29%5Ccdot%20%5Chat%7Bv%7D)
Where
is the unit vector of
, which is determined by the following expression:
![\hat{v} = \frac{\vec v}{\|\vec v \|}](https://tex.z-dn.net/?f=%5Chat%7Bv%7D%20%3D%20%5Cfrac%7B%5Cvec%20v%7D%7B%5C%7C%5Cvec%20v%20%5C%7C%7D)
Where
is the norm of
, whose value can be found by Pythagorean Theorem.
Then, if
and
, then:
![\|\vec v\| =\sqrt{2^{2}+3^{3}}](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20v%5C%7C%20%3D%5Csqrt%7B2%5E%7B2%7D%2B3%5E%7B3%7D%7D)
![\|\vec v\|=\sqrt{13}](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20v%5C%7C%3D%5Csqrt%7B13%7D)
![\hat{v} = \frac{1}{\sqrt{13}} \cdot(2\,i + 3\,j)](https://tex.z-dn.net/?f=%5Chat%7Bv%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B13%7D%7D%20%5Ccdot%282%5C%2Ci%20%2B%203%5C%2Cj%29)
![\hat{v} = \frac{2}{\sqrt{13}}\,i+ \frac{3}{\sqrt{13}}\,j](https://tex.z-dn.net/?f=%5Chat%7Bv%7D%20%3D%20%5Cfrac%7B2%7D%7B%5Csqrt%7B13%7D%7D%5C%2Ci%2B%20%5Cfrac%7B3%7D%7B%5Csqrt%7B13%7D%7D%5C%2Cj)
![\vec F \bullet \hat{v} = (0)\cdot \left(\frac{2}{\sqrt{13}} \right)+(-17)\cdot \left(\frac{3}{\sqrt{13}} \right)](https://tex.z-dn.net/?f=%5Cvec%20F%20%5Cbullet%20%5Chat%7Bv%7D%20%3D%20%280%29%5Ccdot%20%5Cleft%28%5Cfrac%7B2%7D%7B%5Csqrt%7B13%7D%7D%20%5Cright%29%2B%28-17%29%5Ccdot%20%5Cleft%28%5Cfrac%7B3%7D%7B%5Csqrt%7B13%7D%7D%20%5Cright%29)
![\vec F \bullet \hat{v} = -\frac{51}{\sqrt{13}}](https://tex.z-dn.net/?f=%5Cvec%20F%20%5Cbullet%20%5Chat%7Bv%7D%20%3D%20-%5Cfrac%7B51%7D%7B%5Csqrt%7B13%7D%7D)
![\vec F_{\parallel} = \left(-\frac{51}{\sqrt{13}} \right)\cdot \left(\frac{2}{\sqrt{13}}\,i+\frac{3}{\sqrt{13}}\,j \right)](https://tex.z-dn.net/?f=%5Cvec%20F_%7B%5Cparallel%7D%20%3D%20%5Cleft%28-%5Cfrac%7B51%7D%7B%5Csqrt%7B13%7D%7D%20%5Cright%29%5Ccdot%20%5Cleft%28%5Cfrac%7B2%7D%7B%5Csqrt%7B13%7D%7D%5C%2Ci%2B%5Cfrac%7B3%7D%7B%5Csqrt%7B13%7D%7D%5C%2Cj%20%20%5Cright%29)
(b) Parallel and perpendicular components are orthogonal to each other and the perpendicular component can be found by using the following vectorial subtraction:
![\vec F_{\perp} = \vec F - \vec F_{\parallel}](https://tex.z-dn.net/?f=%5Cvec%20F_%7B%5Cperp%7D%20%3D%20%5Cvec%20F%20-%20%5Cvec%20F_%7B%5Cparallel%7D)
Given that
and
, the component of
perpendicular to
is:
![\vec F_{\perp} = -17\,j -\left(-\frac{102}{13}\,i-\frac{153}{13}\,j \right)](https://tex.z-dn.net/?f=%5Cvec%20F_%7B%5Cperp%7D%20%3D%20-17%5C%2Cj%20-%5Cleft%28-%5Cfrac%7B102%7D%7B13%7D%5C%2Ci-%5Cfrac%7B153%7D%7B13%7D%5C%2Cj%20%20%5Cright%29)
![\vec F_{\perp} = \frac{102}{13}\,i + \left(\frac{153}{13}-17 \right)\,j](https://tex.z-dn.net/?f=%5Cvec%20F_%7B%5Cperp%7D%20%3D%20%5Cfrac%7B102%7D%7B13%7D%5C%2Ci%20%2B%20%5Cleft%28%5Cfrac%7B153%7D%7B13%7D-17%20%5Cright%29%5C%2Cj)
![\vec F_{\perp} = \frac{102}{13}\,i -\frac{68}{13}\,j](https://tex.z-dn.net/?f=%5Cvec%20F_%7B%5Cperp%7D%20%3D%20%5Cfrac%7B102%7D%7B13%7D%5C%2Ci%20-%5Cfrac%7B68%7D%7B13%7D%5C%2Cj)
(c) The work done by
through displacement
is:
![W = \vec F \bullet \vec v](https://tex.z-dn.net/?f=W%20%3D%20%5Cvec%20F%20%5Cbullet%20%5Cvec%20v)
![W = (0)\cdot (2)+(-17)\cdot (3)](https://tex.z-dn.net/?f=W%20%3D%20%280%29%5Ccdot%20%282%29%2B%28-17%29%5Ccdot%20%283%29)
![W = -51](https://tex.z-dn.net/?f=W%20%3D%20-51)
U have to *modify it to increase its ground clearance*
If a = k
v = kt + c1
x = kt^2/2 + c1t + c2
which means that the answer is B. quadratic function shape
hope this helps
Answer: because ν = velocity/λ where ν and λ are the frequency and wavelegth of the wave.
Explanation: In order to explain this problem we have to consider the relationship between frequency and wavelengths which are related by the velocity of the wave as follows ν*λ=v where ν and λ are the frequency and wavelegth of the wave. These parameters have an inverse proportionality.
Then, ν = velocity/λ
Explanation:
There are generally two types of collisions between objects - elastic and inelastic.
Elastic collisions are those that converse kinetic energy. Inelastic are those that do not conserve kinetic energy.
In the ideal inelastic collision and elastic collisions, momentum is conserved.
Typically, ideal inelastic collisions are represented when both masses stick together after the collision.
The problem statement gives no indication that this is an ideal inelastic collision (the cars stick together) or an inelastic collision (no energy degradation expression is given). Therefore, we should assume that the cars are experiencing an elastic collision.
Since both momentum and kinetic energy are converved, we can observe that...
![m_1 v_1 + m_2 v_2 = m_1 u_1 + m_2 u_2](https://tex.z-dn.net/?f=m_1%20v_1%20%2B%20m_2%20v_2%20%3D%20m_1%20u_1%20%2B%20m_2%20u_2)
![1/2 m_1 v_1^2 + 1/2 m_2 v_2^2 = 1/2 m_1 u_1^2 + 1/2 m_2 u_2^2](https://tex.z-dn.net/?f=1%2F2%20m_1%20v_1%5E2%20%2B%201%2F2%20m_2%20v_2%5E2%20%3D%201%2F2%20m_1%20u_1%5E2%20%2B%201%2F2%20m_2%20u_2%5E2)
where v is the initial velocity and u is the final velocity (after the collision)
The problem statement gives us three of the four unknowns. So we can easily apply either equation to solve the the velocity of the 1600-kg car after the collision. Momentum is easier to work with.