Answer:
It will take Andy 1.198minutes to mow the lawn and it will take Brian 1,209.98minutes to mow the same lawn.
Step-by-step explanation:
Using the simultaneous equation concept, let A denote Andy and B be Brian
Andy and Brian can mow the lawn for 1212minutes i.e A+B = 1212..eqn 1
If Brian would mow the lawn by himself in 1010 minutes more than it would take Andy, this means B=1010A...eqn 2.
Substituting eqn 2 into eqn 1
Equation 1 becomes
A+1010A=1212
1011A=1212
A=1212/1011
A=1.198
B = 1010×1.198
B=1,209.98
Therefore, It will take Andy 1.198minutes to mow the lawn and it will take Brian 1,209.98minutes to mow the same lawn.
Answer:
(a) 1.16 s
(b)0.861 Hz
Explanation:
(a) Period : The period of a simple harmonic motion is the time in seconds, required for a object undergoing oscillation to complete one cycle.
From the question,
If 1550 cycles is completed in (30×60) seconds,
1 cycle is completed in x seconds
x = 30×60/1550
x = 1.16 s
Hence the period is 1.16 seconds.
(b) Frequency : This can be defined as the number of cycles that is completed in one seconds, by an oscillating body. The S.I unit of frequency is Hertz (Hz).
Mathematically, Frequency is given as
F = 1/T ........................... Equation 1
Where F = frequency, T = period.
Given: T = 1.16 s.
Substitute into equation 1
F = 1/1.16
F = 0.862 Hz
Hence thee frequency = 0.862 Hz
Answer:
50m/s, 187.5m
Explanation:
Consider unit analysis:
m/s² = m/(s×s)
This can be read as "meters per second, per second". From fundamental kinematics, meters per second is the same as saying velocity.
Velocity is being increased per second, and this is called acceleration:
a = v/t, where a is acceleration, v is change of velocity and t is change of time. "Change" is represented by a triangle called delta and (delta)A = A2 - A1
From the question, we have the variables:
a = 5m/s²
(delta)v = v2 - 25m/s
(delta)t = 5s (initial time is 0)
a = v/t
(5m/s^2)=v/5s
25m/s = v2 - 25m/s
50m/s = v2
The final velocity of the vehicle is 50m/s.
A formula exists to find displacement with regards to acceleration:
d=v(initial) × t +1/2 × a × t²
d=25m/s × 5s + 1/2 × 5m/s² ×(5s)²
d=125m+1/2×125m
d=125m+62.5m
d=187.5m
The distance travelled by the vehicle is 192.5m.
<em>One of the most important skills you can have in any science is unit analysis. Treat meters, seconds, moles, etc as </em><em>values</em><em> when doing </em><em>calculations</em><em> </em><em>and see if you get the result you're looking for.</em>
The inner planets are usually rocky because the gravitational pull is stronger closer to the star or in this case the sun. The dust and rocky particles that are left over after a super nova or in a nebula will tend to orbit closer to a proto-star when a solar system is in its early days. In our solar system these planets are Mercury, Venus, Earth and Mars. Gases are less dense and will be less affected by the pull of gravity because rocky particles have more mass. The outer planets are gas giants formed from clouds of gas that would be further out in the spinning disk around a proto-star.
