Given a sphere with radius r, find the height of a pyramid of minimum volume whose base is a square and whose base and triangula
r faces are all tangent to the sphere. What if the base of the pyramid is a regular n-gon? (A regular n-gon is a polygon with n equal sides and angles.) (Use the fact that the volume of a pyramid is V = 1 3Ah, where A is the area of the base.)
1 answer:
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Answer:
18.3 m , 25.4°
Explanation:
d1 = 6 m, θ1 = 40°
d2 = 8 m, θ2 = 30°
d3 = 5 m, θ3 = 0°
Write the displacements in the vector form
The total displacement is given by
magnitude of resultant displacement is given by
d = 18.3 m
Let θ be the angle of resultant displacement with + x axis
θ = 25.4°
Answer:
K.E₂ = mg(h - 2R)
Explanation:
The diagram of the car at the top of the loop is given below. Considering the initial position of the car and the final position as the top of the loop. We apply law of conservation of energy:
K.E₁ + P.E₁ = K.E₂ + P.E₂
where,
K.E₁ = Initial Kinetic Energy = (1/2)mv² = (1/2)m(0 m/s)² = 0 (car initially at rest)
P.E₁ = Initial Potential Energy = mgh
K.E₂ = Final Kinetic Energy at the top of the loop = ?
P.E₂ = Final Potential Energy = mg(2R) (since, the height at top of loop is 2R)
Therefore,
0 + mgh = K.E₂ + mg(2R)
<u>K.E₂ = mg(h - 2R)</u>
