The answer for your problem is shown on the picture.
Answer:
a) Initial angular speed = 30 rad/s
b) Final angular speed = 70 rad/s
Explanation:
a) We have equation of motion s = ut + 0.5at²
Here s = 400 radians
t = 8 s
a = 5 rad/s²
Substituting
400 = u x 8 + 0.5 x 5 x 8²
u = 30 rad/s
Initial angular speed = 30 rad/s
b) We have equation of motion v = u + at
Here u = 30 rad/s
t = 8 s
a = 5 rad/s²
Substituting
v = 30 + 5 x 8 = 70 rad/s
Final angular speed = 70 rad/s
Answer:
The force due to air resistance is 256 N.
Explanation:
Given;
mass of the plane, m = 5 kg
applied force on the plane, Fa = 706 N
the net force on the plane, ∑F= 450 N
Let the force due to air resistance = Fr
The net force on the plane is given as;
Net force = applied force - force due to air resistance
∑F = Fa - Fr
Fr = Fa - ∑F
Fr = 706 - 450
Fr = 256 N.
Therefore, the force due to air resistance is 256 N.
Answer:
t_{out} =
t_{in}, t_{out} = 
Explanation:
This in a relative velocity exercise in one dimension,
let's start with the swimmer going downstream
its speed is

The subscripts are s for the swimmer, r for the river and g for the Earth
with the velocity constant we can use the relations of uniform motion
= D / 
D = v_{sg1} t_{out}
now let's analyze when the swimmer turns around and returns to the starting point

= D / 
D = v_{sg 2} t_{in}
with the distance is the same we can equalize

t_{out} = t_{in}
t_{out} =
t_{in}
This must be the answer since the return time is known. If you want to delete this time
t_{in}= D / 
we substitute
t_{out} = \frac{v_s - v_r}{v_s+v_r} ()
t_{out} = 
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