First, calculate how long the ball is in midair. This will depend only on the vertical displacement; once the ball hits the ground, projectile motion is over. Since the ball is thrown horizontally, it originally has no vertical speed.
t = time vi = initial vertical speed = 0m/s g = gravity = -9.8m/s^2 y = vertical displacement = -45m
y = .5gt^2 [Basically, in this equation we see how long it takes the ball to fall 45m] -45m = .5 (-9.8m/s^2) * t^2 t = 3.03 s
Now we know that the ball is midair for 3.03s. Since horizontal speed is constant we can simply use:
x = horizontal displacement v = horizontal speed = 25m/s t = time = 3.03s
x = v*t x = 25m/s * 3.03s = 75.76 m Thus, the ball goes about 75 or 76 m from the base of the cliff.
Answer:

Explanation:
The heaviside function is defined as:

so we see that the Heaviside function "switches on" when
, and remains switched on when 
If we want our heaviside function to switch on when
, we need the argument to the heaviside function to be 0 when 
Thus we define a function f:

The
term inside the heaviside function makes sure to displace the function 5 units to the right.
Now we just need to add a scale up factor of 240 V, because thats the voltage applied after the heaviside function switches on. (
when
, so it becomes just a 1, which we can safely ignore.)
Therefore our final result is:

I have made a sketch for you, and added it as attachment.
Answer:
Yes the body will receive a dangerous shock in both cases.
Explanation:
Different parts of the body has different resistance. skin has the high resistance as compared to other organs of the body.
Dry skin has high resistance than wet skin this is because water is relatively good conductor of electricity, it adds parallel path to the current flow and hence reduces skin resistance.
Dry hands body has approximately 500 kΩ resistance and if 120 V electricity supply current received will be:
I = V/R= 120/ 500*10^3
I= 0.24 mA
Even the current seems is much lower than the safe zone but this is the case in case of DC voltage in case of AC voltage the body will receive a shock this is because the skin pass more current when the voltage is changing i.e. AC.
Similarly for wet hands body resistance is 1 kΩ. so the current through the body seems to be:
I = 120 / 1000
I = 12 mA
The current is higher than safe zone so the body will receive a dangerous shock.
1 coulomb of electric charge is carried by 6.25 x 10^18 electrons
1 Ampere = 1 coulomb per second
10 A = 10 coulombs per second
(2.0 x 10^20 electrons) x (coul / 6.25 x 10^18 electrons) / (10 coul/sec) =
(2.0 x 10^20) / (6.25 x 10^18 x 10) sec = <em>3.2 seconds</em>
Answer:

Explanation:
initial velocity
magnitude of velocity, v = 12 m/s
angle made of velocity with negative x-axis,θ = 60°
We need to calculate x- component of v

velocity is in negative x-direction, v = -12 m/s
now,



Hence, the velocity x-component is equal to -6 m/s.