Answer:
A) 16.6 m/s i -17.2 m/s j B) 23.9 m/s c) 46º below horizontal.
Explanation:
A) Once released, the football is not under the influence of any external force in the horizontal direction, so it continues moving at a constant speed equal to the initial velocity, i.e., 16.6 m/s.
If we choose the horizontal direction to be coincident with the x-axis, and make positive the direction towards the right (assuming that this was the direction along which the football was thrown), we can write the horizontal component of the veelocity vector, as follows:
vₓ = 16.6 m/s i
In the vertical direction, the football, once released, is in free fall, starting from rest.
So, we can find the vertical component of the velocity vector, at a given point in time, applying the definition of acceleration, as follows:
vy = a*t = -g*t = -9.81 m/s²*1.75 s = -17.2 m/s
Assuming that the upward direction is the positive for the y-axis (perpendicular to the chosen x-axis), we can write the vertical component of the velocity vector, at t=1.75 s, as follows:
vy = -17.2 m/s j
So, the velocity vector, in terms of the unit vectors i and j, can be written in this way:
v = 16.6 m/s i -17.2 m/s j
b) The magnitude of this vector can be found applying trigonometry, as the magnitude is the hypotenuse of a triangle with sides equal to vx and vy, as follows:
v = 23.9 m/s
c) The direction of the vector (below the horizontal) can be found as the angle which tangent is given by the quotient between vy and vx, as follows:
tg θ =
⇒ θ = tg⁻¹ (-1.036) = 46º below horizontal.
Answer:
The new self inductance is 3 times of the initial self inductance.
Explanation:
The self inductance of a solenoid is given by :
Where
N is number of turns per unit length
A is area of cross section
l is length of solenoid
If length and number of coil turns are both tripled,
l' = 3l and N' = 3N
New self inductance is given by :
So, the new self inductance is 3 times of the initial self inductance.
Answer:
a. speed, v = 0.97 c
b. time, t' = 20.56 years
Given:
t' = 5 years
distance of the planet from the earth, d = 10 light years = 10 c
Solution:
(a) Distance travelled in a round trip, d' = 2d = 20 c = L'
Now, using Length contraction formula of relativity theory:
(1)
time taken = 5 years
We know that :
time =
5 = (2)
Dividing eqn (1) by v on both the sides and substituting eqn (2) in eqn (1):
Squaring both the sides and Solving above eqution, we get:
v = 0.97 c
(b) Time observed from Earth:
Using time dilation:
Solving the above eqn:
t'' = 20.56 years
The distance between slit and the screen is 1.214m.
To find the answer, we have to know about the width of the central maximum.
<h3>How to find the distance between slit and the screen?</h3>
where, d is the distance between slit and the screen, and a is the slit width.
Thus, we can conclude that, the distance between slit and the screen is 1.214m.
Learn more about the width of the central maximum here:
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