The circumference of a circle is (pi) x (diameter)
The circumference of the cupcake is (pi) x (5 cm)
Halfway around is (1/2) x (pi) x (5 cm) = (2.5 pi cm) = <em>about 7.85 cm</em>
The 'why' appears up above, in the first 2 lines of this solution.
Answers:
a) 30 m/s
b) 480 N
Explanation:
The rest of the question is written below:
a. What is the final speed of the falcon and pigeon?
b. What is the average force on the pigeon during the impact?
<h3>a) Final speed</h3>
This part can be solved by the Conservation of linear momentum principle, which establishes the initial momentum
before the collision must be equal to the final momentum
after the collision:
(1)
Being:


Where:
the mas of the peregrine falcon
the initial speed of the falcon
is the mass of the pigeon
the initial speed of the pigeon (at rest)
the final speed of the system falcon-pigeon
Then:
(2)
Finding
:
(3)
(4)
(5) This is the final speed
<h3>b) Force on the pigeon</h3>
In this part we will use the following equation:
(6)
Where:
is the force exerted on the pigeon
is the time
is the pigeon's change in momentum
Then:
(7)
(8) Since 
Substituting (8) in (6):
(9)
(10)
Finally:

Explanation:
the object will begin to move
Answer:
M1 V1 = M1 V2 + M2 V3 conservation of momentum
V2 = (M1 V1 - M2 V3) / M1 where V2 = speed of M1 after impact
V2 = (3 * 9 - 1.5 * 5) / 9 = (27 - 7.5) / 9 = 2.17 m/s
Note: All speeds are in the same direction and have the same sign
Given :
The focal length of a concave mirror is 18 cm.
To Find :
The radius of curvature of the concave mirror.
Solution :
We know,

Therefore, the radius of curvature of concave mirror is 36 cm.
Hence, this is the required solution.