(a) Differentiate the position vector to get the velocity vector:
<em>r</em><em>(t)</em> = (3.00 m/s) <em>t</em> <em>i</em> - (4.00 m/s²) <em>t</em>² <em>j</em> + (2.00 m) <em>k</em>
<em>v</em><em>(t)</em> = d<em>r</em>/d<em>t</em> = (3.00 m/s) <em>i</em> - (8.00 m/s²) <em>t</em> <em>j</em>
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(b) The velocity at <em>t</em> = 2.00 s is
<em>v</em> (2.00 s) = (3.00 m/s) <em>i</em> - (16.0 m/s) <em>j</em>
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(c) Compute the electron's position at <em>t</em> = 2.00 s:
<em>r</em> (2.00 s) = (6.00 m) <em>i</em> - (16.0 m) <em>j</em> + (2.00 m) <em>k</em>
The electron's distance from the origin at <em>t</em> = 2.00 is the magnitude of this vector:
||<em>r</em> (2.00 s)|| = √((6.00 m)² + (-16.0 m)² + (2.00 m)²) = 2 √74 m ≈ 17.2 m
(d) In the <em>x</em>-<em>y</em> plane, the velocity vector at <em>t</em> = 2.00 s makes an angle <em>θ</em> with the positive <em>x</em>-axis such that
tan(<em>θ</em>) = (-16.0 m/s) / (3.00 m/s) ==> <em>θ</em> ≈ -79.4º
or an angle of about 360º + <em>θ</em> ≈ 281º in the counter-clockwise direction.
Answer:
5.125
Explanation:
formula for speed is distance/time distance measured in metres
Answer:
T = 1010 degree Celsius
Explanation:
mass of ball (Mb) = 100 g
mass of water (Mw) = 400 g
temp of water = 0 degree
specific heat of platinum (C) = 0.04 cal/g degree celsius
we can calculate the temperature of the furnace from the equation before
Mb x C x (temp of furnace (T) - equilibrium temp) = Mw x (equilibrium temp - temp of furnace)
100 x 0.04 x ( T - 10) = 400 x (10 - 0)
4 (T - 10) = 4000
T - 10 = 1000
T = 1010 degree Celsius
Answer:
The current would be same in both situation.
Explanation:
Given that,
Current I = 13 A
Number of turns = 23
We need to calculate the induced emf
Using formula of induced emf is
For N = 1
We need to calculate the current
Using formula of current
Put the value of emf
Now, if the number of turn is 22 , then induced emf would be
Then the current would be
Hence, The current would be same in both situation.
Answer:
24.531 m
Explanation:
t = Time taken = 1.7 s
u = Initial velocity = 6.1 m/s
v = Final velocity
s = Displacement
g = Acceleration due to gravity = 9.81 m/s² = a
Equation of motion
The initial height of the rock above the ground is 24.531 m