<span>Answer:
F(x) = ax^2 - bx
or
F(x) = ax² - bx
F(x) = 30x² - 6x
â«F(x)dx = â«(30x² - 6x)dx
as this is evaluated from zero to x
W = 10x³ - 3x² <===ANS
W = 10(0.42³) - 3(0.42²) - [10(0³) - 3(0²)]
W = 0.212 J <===ANS
W = 10(0.72³) - 3(0.72²) - [10(0.42³) - 3(0.42²)]
W = 1.966 J <===ANS</span>
Construct a vector diagram. It will be a right-angled triangle. One vector (the hypotenuse) represents the heading of the boat, one represents the current and one represents the resultant speed of the boat, which I'll call x. Their magnitudes are 20, 3 and x. Let the required angle = theta. We have:
<span>theta = arcsin(3/20) = approx. 8.63° </span>
<span>The boat should head against the current in a direction approx. 8.63° to the line connecting the dock with the point opposite, or approx. 81.37° to the shore line. </span>
<span>x = sqrt(20^2 - 3^2) </span>
<span>= sqrt(400 - 9) </span>
<span>= sqrt 391 </span>
<span>The boat's crossing time = </span>
<span>0.5 km/(sqrt 391 km/hr) </span>
<span>= (0.5/sqrt 391) hr </span>
<span>= approx. 0.025 hr </span>
<span>= approx. 91 seconds</span>
Answer:

Explanation:
The elastic potential energy of a spring is given by
, where
is the spring constant of the spring and
is displacement from point of equilibrium.
When released, this potential energy will be converted into kinetic energy. Kinetic energy is given by
, where
is the mass of the object and
is the object's velocity.
Thus, we have:

Substituting given values, we get:

Answer:
The time it takes the ball to stop is 0.021 s.
Explanation:
Given;
mass of the softball, m = 720 g = 0.72 kg
velocity of the ball, v = 15.0 m/s
applied force, F = 520 N
Apply Newton's second law of motion, to determine the time it takes the ball to stop;

Therefore, the time it takes the ball to stop is 0.021 s.
Answer:
3. Higher in some places and lower in other places