Answer:
θ = 20.9 rad
Explanation:
In a blender after a short period of acceleration the blade is kept at a constant angular velocity, for which we can use the relationship
w = θ / t
θ = w t
if we know the value of the angular velocity we can find the angular position, we must remember that all the angles must be in radians
suppose that the angular velocity is w = 10 rpm, let us reduce to the SI system
w = 10 rpm 
= 1,047 rads
let's calculate
θ = 1,047 20
θ = 20.9 rad
The strength of the fireman in vertical direction will be given by F = m * g. Then, the work done will be given by definition by W = F * d. Substituting the expression of the Force in that of the work, we have that the work will be W = m * g * d. Substituting the given values and assuming that g = 10m / s ^ 2, we have a total work of W = (73) * (10) * (9) = 6570 J
Answer:
In a time-position graph (s-t graph):
slope = velocity
In a time-velocity graph (v-t graph):
slope = acceleration
area under graph = change in displacement (distance travelled)
In a time-acceleration graph (a-t graph):
area under graph = change in velocity
The final velocity of the projectile when it strikes the ground below is 198.51 m/s.
<h3>
Time of motion of the projectile</h3>
The time taken for the projectile to fall to the ground is calculated as follows;
h = vt + ¹/₂gt²
where;
- h is height of the cliff
- v is velocity
- t is time of motion
265 = (185 x sin45)t + (0.5)(9.8)t²
265 = 130.8t + 4.9t²
4.9t² + 130.8t - 265 = 0
solve the quadratic equation using formula method,
t = 1.89 s
<h3>Final velocity of the projectile</h3>
vyf = vyi + gt
where;
- vyf is the final vertical velocity
- vyi is initial vertical velocity
vyf = (185 x sin45) + (9.8 x 1.89)
vyf = 149.322 m/s
vxf = vxi
where;
- vxf is the final horizontal velocity
- vxi is the initial horizontal velocity
vxf = 185 x cos(45)
vxf = 130.8 m/s
vf = √(vyf² + vxf²)
where;
- vf is the speed of the projectile when it strikes the ground below
vf = √(149.322² + 130.8²)
vf = 198.51 m/s
Learn more about final velocity here: brainly.com/question/6504879
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Answer: 
Explanation:
We are told both planets describe a circular orbit around the star S. So, let's approach this problem begining with the angular velocity 
of the planet P1 with a period 
:
(1)
Where:
is the velocity of planet P1
is the radius of the orbit of planet P1
Finding :
(2)
(3)
(4)
On the other hand, we know the gravitational force 
between the star S with mass 
and the planet P1 with mass 
is:
(5)
Where 
is the Gravitational Constant and its value is 
In addition, the centripetal force 
exerted on the planet is:
(6)
Assuming this system is in equilibrium:
(7)
Substituting (5) and (6) in (7):
(8)
Finding :
(9)
(10)
Finally:
(11) This is the mass of the star S
