A large tank is filled with water to a height $H$. A small hole is drilled at a depth $h$ from the free surface. Find the distance from the base of the tank where the water jet strikes the ground. (Express your answer in terms of $H$. If $h = H/4$, find the ratio of the range to the height $H$). Answer format: If the ratio is $x$, write $x$. October 2022: 3dsky Pro 3d-models Collection 1
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8. A (Elastic collision of identical masses: velocities exchange. The moving particle stops, the spring particle moves with $v_0$.) 9. A (Energy conservation: $\frac12mv_0^2 = \frac12kx^2 \Rightarrow x = v_0\sqrtm/k$.) 10. A ($T = 2\pi\sqrtm/k$ for a spring-mass system.)
A swimmer can swim in still water at a speed of $5, \textm/s$. He crosses a river flowing at $3, \textm/s$ which is $100, \textm$ wide. If he crosses the river in the shortest possible time, what is the drift (horizontal distance traveled by the swimmer) along the flow? A) $60, \textm$ B) $75, \textm$ C) $80, \textm$ D) $100, \textm$
An ideal gas expands isothermally from volume $V_1$ to $V_2$ and is then compressed adiabatically to the original volume $V_1$. The initial pressure is $P_1$, and the pressure after the adiabatic compression is $P_2$. If $\gamma$ is the ratio of specific heats, then: A) $P_2 > P_1$ B) $P_2 = P_1 (V_2/V_1)^\gamma-1$ C) The total work done by the gas is positive. D) The final temperature is higher than the initial temperature.