Question

Камни Из жерла вулкана вылетают вверх На высоту 200м. С какой начальной скоростью они летят и через какое время падают обратно

Answer 1

H=200 м    vo=?    t=?
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vo=√(2*g*h)=√(2*10*200)≈63.2 м/с
t=vo/g=63.2/10=6.32 c
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Answer 2

Initial Assumptions

To calculate the initial velocity and time taken for the stones to fall back down, we can make some assumptions: 1. We'll assume that the stones are projected vertically upwards with an initial velocity. 2. We'll neglect air resistance for simplicity.

Calculating Initial Velocity

To calculate the initial velocity with which the stones are projected upwards, we can use the following kinematic equation: $$v_f = v_i - gt$$ Where: - $v_f$ = final velocity (0 m/s at the highest point) - $v_i$ = initial velocity - $g$ = acceleration due to gravity (approximately 9.81 m/s^2) - $t$ = time taken to reach the highest point

Solving for $v_i$: $$0 = v_i - (9.81 \, m/s^2) \times t$$ $$v_i = 9.81 \, m/s^2 \times t$$

Time Taken to Fall Back Down

The time taken for the stones to fall back down can be calculated using the following equation: $$t_{total} = 2t$$ Where: - $t_{total}$ = total time taken for the stones to fall back down - $t$ = time taken to reach the highest point

Let's calculate the initial velocity and time taken for the stones to fall back down.