Answer:
1/8 = (1/2)^3
This implies the sample has decayed for 3 half lives
3 * 5730 yrs = 17,200 years
Answer:
Distance will be 49.34 m
Explanation:
We have given wavelength 
Diameter of the antenna d = 2.7 m
Range L = 7.8 km = 7800 m
We have to find the smallest distance hat two speedboats can be from each other and still be resolved as two separate objects D
We know that distance is given by 
So distance D will be 49.34 m
Answer:
The acceleration of the train is 5 m/s².
Explanation:
Given:
let the initial velocity of a train = 5 m/s and
final velocity of a train = 45 m/s
time taken = 8 s
To find:
acceleration: ?
Solution:
We define acceleration as change in velocity per unit time that is the difference between the final velocity and initial velocity divided by time.

On substituting the above values we get the required acceleration

Therefore,the acceleration of the train is 5 m/s².
Hi there!
We can begin by solving for the linear acceleration as we are given sufficient values to do so.
We can use the following equation:
vf = vi + at
Plug in given values:
4 = 9.7 + 4.4a
Solve for a:
a = -1.295 m/s²
We can use the following equation to convert from linear to angular acceleration:
a = αr
a/r = α
Thus:
-1.295/0.61 = -2.124 rad/sec² ⇒ 2.124 rad/sec² since counterclockwise is positive.
Now, we can find the angular displacement using the following:
θ = ωit + 1/2αt²
We must convert the initial velocity of the tire (9.7 m/s) to angular velocity:
v = ωr
v/r = ω
9.7/0.61 = 15.9 rad/sec
Plug into the equation:
θ = 15.9(4.4) + 1/2(2.124)(4.4²) = 20.56 rad