Answer:
The function has a maximum in 
The maximum is:

Explanation:
Find the first derivative of the function for the inflection point, then equal to zero and solve for x




Now find the second derivative of the function and evaluate at x = 3.
If
the function has a maximum
If
the function has a minimum

Note that:

the function has a maximum in 
The maximum is:

M = W/g
mass (m)
weight (W) and strength of gravity (g)
Therefore the mass of the astronaut is 65 kilograms
Answer:
Distance travel by go-cart = 500 meter
Explanation:
Given:
Speed of go cart = 25 m/s
Time travel = 20 seconds
Find:
Distance travel by go-cart
Computation:
Distance = Speed x time
Distance travel by go-cart = Speed of go cart x Time travel
Distance travel by go-cart = 25 x 20
Distance travel by go-cart = 500 meter
Answer:

Explanation: Weight of space probes on earth is given by:
W= weight of the object( in N)
m= mass of the object (in kg)
g=acceleration due to gravity(9.81
)
Therefore,


Similarly,


Now, considering these two parts as uniform spherical objects
Also, according to Superposition principle, gravitational net force experienced by an object is sum of all individual forces on the object.
Force between these two objects is given by:

G= gravitational constant (
)
= masses of the object
R= distance between their centres (in m)(18 m)
Substituiting all these values into the above formula

This is the magnitude of force experienced by each part in the direction towards the other part, i.e the gravitational force is attractive in nature.
a.) K 2=K 1 +GmM( r 21− r 11)=2.2×10 7J
b.) K 2 +GmM( r 11− r 21)=6.9×10 7 J
Applying Law of Energy conservation :
K 1+U 1
=K 2+U 2
⇒K 1− r 1GmM
=K 2− r 2 GmM
where M=5.0×10 23kg,r1
=> R=3.0×10 6m and m=10kg
(a) If K 1
=5.0×10 7J and r 2
=4.0×10 6 m, then the above equation leads to
K 2=K 1 +GmM (r 21− r 11)=2.2×10 7J
(b) In this case, we require K 2
=0 and r2
=8.0×10 6m, and solve for K 1:K 1
=K 2 +GmM (r 11− r 21)=6.9×10 7 J
Learn more about Kinetic energy on:
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