Answer:

Definition:
Half-life- The time taken for half of the radioactive isotopes to decay.
Explanation:
How does radioactive decay work? Radioactive decay is a process by which unstable nuclei become more stable through the emission of alpha or beta particles or gamma rays.
Since a half-life is the time taken for half of the isotopes to decay, we can simply divide the initial mass of 100 grams by 2; this gives us 50 grams.
1) Divide 100g by 2.

Answer:

Explanation:
Given
-- initial velocity
--- height
Required
Determine the time to hit the ground
This will be solved using the following motion equation.

Where

So, we have:


Subtract 30.2 from both sides





Solve using quadratic formula:

Where




Split the expression
or 
or 
Time can't be negative; So, we have:


Hence, the time to hit the ground is 1.82 seconds
Answer:

Explanation:
In this case, since the charged particle moves in circular motion, the centripetal force is equivalent to the magnetic force.

Answer:
C. 30.6m
Explanation:
To find the height of the tower, we are to use Newtons law of motion to solve this problem. Since the penny is falling from the top of the tower, it is acted by the acceleration due to gravity. The formula to be used is:

Where H is the height of the tower, t is the time taken to hit the ground, u is the initial velocity and g is the acceleration due to gravity.
Given that, t = 2.5 s, g =9.8 m/s², u = 0 m/s (at the top of tower)

A) 1 rev = 2π rad. Using this ratio, you can find the rad/s: 1160 rev/min x 2π rad/rev x 1 min/60 s = 121.5 rad/s
b) You can find linear speed from angular speed using this equation (note the radius is half the diameter given in the question): v = ωr = 121.5 rad/s x 1.175 m = 142.8 m/s
c) You can find centripetal acceleration using this equation: a = v^2/r = (142.8 m/s)^2 / 1.175 m = 17 355 m/s^2