Question

Тело брошено со скоростью 15 м/с с балкона, находящегося на высоте 40 м. Чему равна его скорость на высоте 20 м?

Answer 1

H=40 м   h=20 м    vo=15 м/с   v=?
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Δh=H-h=40-20=20 м
Δh=(v²-vo²)/(2*g)
v=√(2*g*Δh+vo²)=√(2*10*20+15²)=25 м/с
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Answer 2

Calculation of the Body's Velocity at a Height of 20m

To calculate the velocity of the body at a height of 20m, we can use the principle of conservation of mechanical energy. According to this principle, the total mechanical energy of the body remains constant throughout its motion, neglecting air resistance.

The total mechanical energy of the body is the sum of its kinetic energy (KE) and potential energy (PE). The kinetic energy is given by the formula KE = (1/2)mv^2, where m is the mass of the body and v is its velocity. The potential energy is given by the formula PE = mgh, where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height.

At the initial height of 40m, the body has an initial velocity of 15 m/s. Using this information, we can calculate the initial kinetic energy (KEi) and potential energy (PEi) of the body:

KEi = (1/2)mv^2 = (1/2)m(15^2) = 112.5m PEi = mgh = m(9.8)(40) = 392mh

The total mechanical energy (Ei) at the initial height is the sum of the initial kinetic energy and potential energy:

Ei = KEi + PEi = 112.5m + 392mh

At a height of 20m, we can calculate the final velocity (vf) using the total mechanical energy at the initial height and the potential energy at the final height (PEf):

Ei = Ef 112.5m + 392mh = KEf + PEf 112.5m + 392mh = (1/2)mvf^2 + mghf

Since the body is at rest at a height of 20m, the final kinetic energy (KEf) is zero. Therefore, the equation becomes:

112.5m + 392mh = 0 + mghf 112.5 + 392h = ghf 112.5 + 392(40) = 9.8hf 112.5 + 15680 = 9.8hf 15892.5 = 9.8hf hf = 15892.5 / 9.8 hf ≈ 1620.51 m

Now, we can calculate the final velocity (vf) using the formula vf = sqrt(2ghf):

vf = sqrt(2 * 9.8 * 1620.51) vf ≈ 179.14 m/s

Therefore, the velocity of the body at a height of 20m is approximately 179.14 m/s.