Suppose you are driving a car and your friend, who is with you in the car, tosses a softball up and down from her point of view.
1 answer:
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Complete Question
An astronaut stands by the rim of a crater on the moon, where the acceleration of gravity is 1.62 m/s2. To determine the depth of the crater, she drops a rock and measures the time it takes for it
to hit the bottom. If the time is 6.3 s, what is the depth of the crater?
Answer:
The depth is 32 m
Explanation:
From the question we are told that
The time is t = 6.3 s
The acceleration due to gravity is
Generally from kinematic equation
Here the u is the initial velocity and the value is 0 m/s
Answer:
λ₂ = 357.3 nm
Explanation:
The expression for double-slit interference is
d sin θ = m λ constructive interference
d sin θ = (m + ½) λ destructive interference.
The initial data corresponds to a constructive interference, they indicate that we are in the fourth order (m = 4), let's look for the separation of the slits
d sin θ = m λ₁
now ask for destructive interference for m = 4
d sin θ = (m + ½) λ₂
we match these two expressions
m λ₁ = (m + ½) λ₂
λ₂ = ( m / m + ½) λλ₁
let's calculate
λ₂ =
λ₂ = 357.3 nm
Answer:
The tension in the cable = 993.5 N
The tension in the cable 496.75 N
The tension in the cable = 248.375 N
Explanation:
The diagram attached below depicts the full understanding of what the question is all about.
Now, obtaining the length of cable 1 from the diagram; we have:
where;
= distance from the fixed point to point B
= distance from the fixed point to pulley A
From the cable 2 as well.we obtain its length
where :
distance from the fixed point to the weight attached to the pulley
Let differentiate equation (1) in order to deduce a relation between the velocities of A and B with respect to time ;
Since is constant ; Then:
where;
velocity at point B
= velocity at pulley A
Let differentiate equation (2) as well in order to deduce a relation between the velocities of W and A with respect to time :
Since is constant ; Then:
where;
the velocity of the weight
Let differentiate equation (3) in order to deduce a relation between accelerations A and B with respect to time
where;
= acceleration at A
acceleration at B
Replacing 0.5 m/s ² for in equation (5); then
Let differentiate equation (4) in order to deduce a relation between W and A with respect to time
where;
= acceleration of weight W
Replacing - 0.25 m/s² for
From the second diagram, if we consider the equilibrium of forces acting on the cylinder in y-direction; we have:
where;
m= mass of the cylinder = 100 kg
= tension in the string = ???
g = acceleration due to gravity = 9.81 m/s²
= acceleration of the cylinder =
Plugging all values into above equation; we have
(100 × 9.81) - = 100(-0.125)
= 993.5 N
∴ The tension in the cable = 993.5 N
From the third diagram, if we consider the equilibrium of forces acting on the cylinder in y-direction on the pulley ; we have:
where ;
= tension in cable 2
Replacing 993.5 N for ; we have
∴ The tension in the cable
From the fourth diagram, if we consider the equilibrium of forces acting on the cylinder in y-direction on the pulley A ; we have
where;
= tension in cable 1
Replacing 496.75 N for in the above equation; we have:
= 248.375 N
∴ The tension in the cable = 248.375 N
