Answer:
θ = 41.8º
Explanation:
This is an internal total reflection exercise, the equation that describes this process is
sin θ = n₂ / n₁
where n₂ is the index of the incident medium and n₁ the other medium must be met n₁> n₂
θ = sin⁻¹ n₂ / n₁
let's calculate
θ = sin⁻¹ (1.00 / 1.50)
θ = 41.8º
This calculus problem can be solved by defining the appropriate variables, constructing a relationship using trigonometry, taking the derivative of both sides with respect to time, and solving for the rate of change of the angle with respect to time. The initial distances, rocket's speed, and angle are used to determine the rocket's position after 3 minutes and thus the rate at which the angle is changing.
This problem involves the concept of related rates in calculus and the understanding of trigonometric relationships. Let's denote the rocket's altitude as y and the angle between the ground and the telescope as θ. We know Δy/Δt = 1300 km/hr, we're given the initial distance (13 km), and we want to find Δθ/Δt at 3 min after lift-off.
From trigonometry, we know that tan(θ) = y/x, where x is the horizontal distance (which remains constant at 13 km) and y is the vertical distance (which is changing). Differentiating both sides with respect to t gives sec²(θ) * Δθ/Δt = Δy/Δt / x. Assuming that the speed of the rocket remains constant, we find that y = (1300 km/hr * 3min)*(1hr/60min) = 65 km at 3 min after launch. Plugging x = 13 km and y = 65 km into the equation tan(θ) = y/x, we get θ = atan(65/13) = 78.69°. Now we can solve for Δθ/Δt using the differentiated equation: Δθ/Δt = ( Δy/Δt / x ) / sec²(θ) = (1300 km/hr / 13 km) / sec²(78.69°). Solving this gives the rate of change of θ with respect to time.
#SPJ12
The combined gas law has no official founder; it is simply the incorporation of the three laws that was discovered. The combined gas law is a gas law that combines Gay-Lussac’s Law, Boyle’s Law and Charle’s Law. Boyle’s law states that pressure is inversely proportional with volume at constant temperature. Charle’s law states that volume is directly proportional with temperature at constant pressure. And Gay-Lussac’s law shows that pressure is directly proportional with temperature at constant volume. The combination of these laws known now as combined gas law gives the ratio between the product of pressure-volume and the temperature of the system is constant. Which gives PV/T=k(constant). When comparing a substance under different conditions, the combined gas law becomes P1V1/T1 = P2V2/T2.
kilograms
Answer:
mass=56.12kg
Explanation:
PE=mgh
4620=m×9.8×8.4
make msubject of the formula...
m =4620/(9.8×8.4)
m=4620/82.32
m=56.12kg
Answer:
the magnet or electric current produces a magnetic field
Explanation:
this magnetic field can be visualized as a pattern of a circular field lines surrounding a wire. hall probes can determine the magnitude of the field
hope it helps you
Answer:Bohr placed the electrons in distinct energy levels. Rutherford described the atom as consisting of a tiny positive mass surrounded by a cloud of negative electrons. Bohr thought that electrons orbited the nucleus in quantised orbits.
Explanation: also rutherfords was just a hypothesis while Bhor took the time to make his an experiment
actually use by the time the water reaches its final temperature?