Answer:
Explanation:
Using the pythagoras theorem, the displacement is expressed as;
d² = x²+y²
y = 36m (north)
x = 20m east
Substitute;
d² = 36²+20²
d² = 1296+400
d² = 1696
d = √1696
d = 41.18m
For the direction;
theta = tan^-1(y/x)
theta = tan^-1(36/20)
theta = tan^-1(1.8)
theta = 60.95°
Hence the magnitude is 41.18m and the direction is 60.95°
Answer:
vf = 3.27[m/s]
Explanation:
In order to solve this problem we must analyze each body individually and find the respective equations. The free body diagram of each body (box and bucket) should be made, in the attached image we can see the free body diagrams and the respective equations.
With the first free body diagram, we determine that the tension T should be equal to the product of the mass of the box by the acceleration of this.
With the second free body diagram we determine another equation that relates the tension to the acceleration of the bucket and the mass of the bucket.
Then we equalize the two stress equations and we can clear the acceleration.
a = 3.58 [m/s^2]
As we know that the bucket descends 1.5 [m], this same distance is traveled by the box, as they are connected by the same rope.
![x = \frac{1}{2} *a*t^{2}\\1.5 = \frac{1}{2}*(3.58) *t^{2} \\t = 0.91 [s]](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2Aa%2At%5E%7B2%7D%5C%5C1.5%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A%283.58%29%20%2At%5E%7B2%7D%20%5C%5Ct%20%3D%200.91%20%5Bs%5D)
And the speed can be calculated as follows:
![v_{f}=v_{o}+a*t\\v_{f}=0+(3.58*0.915)\\v_{f}= 3.27[m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%3Dv_%7Bo%7D%2Ba%2At%5C%5Cv_%7Bf%7D%3D0%2B%283.58%2A0.915%29%5C%5Cv_%7Bf%7D%3D%203.27%5Bm%2Fs%5D)
Answer:
The change in current at
is 
Explanation:
From the question we are told that
The resistance is 
The current is 
The change in voltage with respect to time is 
The change in resistance with time is 
According to ohm's law

differentiating with respect to time using chain rule

substituting value at R = 456


Answer:
Explanation:
Given that,
Magnetic field of 0.24T
B = 0.24T
Field perpendicular to plane i.e 90°
Rate of decrease of length of side of square is 5.4cm/s
dL/dt = 5.4cm/s = 0.054m/s
Since it is decreasing
Then, dL/dt = -0.054m/s
When L is 14cm, what is the EMF induced?
L = 14cm = 0.14m
EMF is give as
ε = - dΦ/dt
Where flux is given as
Φ = BA
Where A is the area of the square
A = L²
Then, Φ = BL²
Substituting this into the EMF
ε = - dΦ/dt
ε = - d(BL²)/dt
B is constant
ε = - Bd(L²)/dt
ε = -2BL dL/dr
ε = -2 × 0.24 × 0.14 × -0.054
ε = 3.63 × 10^-3 V
ε = 3.63mV