Answer:
Explanation:
height fallen = h , initial speed u = 0
time t = 2.4s
h = 1/2 x gt²
= .5 x 9.8 x 2.4²
= 28.22 m
Speed of striking the ground
v = gt
= 9.8 x 2.4
= 23.52 m/s
A ) When rock is thrown upwards
initial velocity u = - 19 m/s
g = 9.8 m/s²
h = ut + 1/2 gt²
50 = - 19t + .5 x 9.8 t²
4.9 t² - 19 t - 50 = 0
=5.7 s
B )
V = - -u+gt
= - 19 + 9.8 x 5.7
= 36.86 m/s
The starting angle θθ of a pendulum does not affect its period for θ<<1θ<<1. At higher angles, however, the period TT increases with increasing θθ.
The relation between TT and θθ can be derived by solving the equation of motion of the simple pendulum (from F=ma)
−gsinθ=lθ¨−gainθ=lθ¨
For small angles, θ≪1,θ≪1, and hence sinθ≈θsinθ≈θ. Hence,
θ¨=−glθθ¨=−glθ
This second-order differential equation can be solved to get θ=θ0cos(ωt),ω=gl−−√θ=θ0cos(ωt),ω=gl. The period is thus T=2πω=2πlg−−√T=2πω=2πlg, which is independent of the starting angle θ0θ0.
For large angles, however, the above derivation is invalid. Without going into the derivation, the general expression of the period is T=2πlg−−√(1+θ2016+...)T=2πlg(1+θ0216+...). At large angles, the θ2016θ0216 term starts to grow big and cause
It is required an infinite work. The additional electron will never reach the origin.
In fact, assuming the additional electron is coming from the positive direction, as it approaches x=+1.00 m it will become closer and closer to the electron located at x=+1.00 m. However, the electrostatic force between the two electrons (which is repulsive) will become infinite when the second electron reaches x=+1.00 m, because the distance d between the two electrons is zero:
So, in order for the additional electron to cross this point, it is required an infinite amount of work, which is impossible.