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Question

If a projectile is fired with an initial velocity u at an angle θ from the horizontal, for what time does it remain in the air?


Solution

Vertical component of initial velocity, uy=u sinθ
At the highest point, vertical component of velocity will become zero.
From the first equation of motion, v=u+at0=uygt0=u sinθgtt=usinθg
Time of flight, T=2t=2u sin θg

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The only electron in the hydrogen atom resides under ordinary conditions on the first orbit. When energy is supplied, the electron moves to higher energy orbit depending on the amount of energy absorbed. When this electron returns to any of the lower orbits, it emits energy. Lyman series is formed when the electron returns to the lowest orbit while Balmer series is formed when the electron returns to second orbit. Similarly, Paschen, Brackett and Pfund series are formed when electron returns to the third, fourth and fifth orbits from higher energy orbits respectively. The maximum number of lines produced when an electron jumps from nth level to ground level is equal Maximum number of lines produced when an electron jumps from nth level to ground level is equal to. 1(n1)2. For example, in the case of n=4, number of lines produces is 6. (43,42,41,32,31,21). When an electron returns from to state, the number of lines in the spectrum will be equal to (n2n1)(n2n1+1)2 If the electron comes back from energy level having energy to energy level having energy, then the difference may be expressed in the terms of energy of photon as E2E1ΔE,λ=hcΔE  Since h and c are constants, ΔE corresponds to definite energy; thus each transition from one energy level to another will produce a light of definite wavelength. This is observed as a line in the spectrum of the hydrogen atom. Wavenumber of line is given by the formula ¯v=(1n211n22). where R is a Rydberg's constant (R=1.1×107m1)

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