We know that the Pythagorean theorem applies only to right triangles, therefore the original vectors must be parallel to the legs of a right triangle.
In other words, they must be orthogonal (i.e. perpendicular to each other) in order that the Pythagorean theorem applies.
That is an Elastic collision
Answer:d
Explanation:
Given
First car is moving towards east with velocity 20 m/s
then it turns towards north then velocity is
suppose car takes t sec to change its path so average acceleration is given by
So average acceleration is towards North of west.
<span>f(x) = 5.05*sin(x*pi/12) + 5.15
First, you need to determine the period of the function. The period will be the time interval between identical points on the sinusoidal function. For this problem, the tide is rising and at 5.15 at midnight for two consecutive days. So the period is 24 hours. Over that 24 hour period, we want the parameter passed to sine to range from 0 to 2*pi. So the scale factor for x will be 2*pi/24 = pi/12 which is approximately 0.261799388. The next thing to note is the magnitude of the wave. That will simply be the difference between the maximum and minimum values. So 10.2 ft - 0.1 ft = 10.1 ft. And since the value of sine ranges from -1 to 1, we need to divide that magnitude by 2, so 10.1 ft / 2 = 5.05 ft.
So our function at this point looks like
f(x) = 5.05*sin(x*pi/12)
But the above function ranges in value from -5.05 to 5.05. So we need to add a bias to it in order to make the low value equal to 0.1. So 0.1 = X - 5.05, 0.1 + 5.05 = X, 5.15 = X. So our function now looks like:
f(x) = 5.05*sin(x*pi/12) + 5.15
The final thing that might have been needed would have been a phase correction. With this problem, we don't need a phase correction since at X = 0 (midnight), the value of X*pi/12 = 0, and the sine of 0 is 0, so the value of the equation is 5.15 which matches the given value of 5.15. But if the problem had been slightly different and the height of the tide at midnight has been something like 7 feet, then we would have had to calculate a phase shift value for the function and add that constant to the parameter being passed into sine, making the function look like:
f(x) = 5.05*sin(x*pi/12 + C) + 5.15
where
C = Phase correction offset.
But we don't need it for this problem, so the answer is:
f(x) = 5.05*sin(x*pi/12) + 5.15
Note: The above solution assumes that angles are being measured in radians. If you're using degrees, then instead of multiplying x by 2*pi/24 = pi/12, you need to multiply by 360/24 = 15 instead, giving f(x) = 5.05*sin(x*15) + 5.15</span>
<u>Final Velocity = 14m/s</u>
<u>Displacement = 56m</u>
Explanation:
U (initial velocity) = 2m/s
A (acceleration) = 3m/s^2
T (time) = 4s
v (final velocity) = ?
S (displacement) = ?
<u>FIRST FIND FINAL VELOCITY:</u>
(i) Multiply both sides by t:
(ii) Add u to both sides:
(iii) rearrange formula:
v = ( 3 × 4 ) + 2
v = 12 + 2
<u>v = 14m/s</u>
<u>SECOND FIND DISPLACEMENT:</u>
(i) Multiply both sides by t:
(ii) Rearrange formula:
s = 14 × 4
<u>s = 56m</u>
Not sure why it isn't one of the options but im pretty sure I did all the steps right...