Which of the following is a rational number? square root of 36, square root of 37, square root of 38, square root of 39 square r
2 answers:
You might be interested in
Answer:
Step-by-step explanation:
Component form of a vector is given by , where
represents change in x-value and
represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector
, the magnitude is
.
190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being , one leg being
, and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.
In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.
Therefore, we have:
To find the other leg, , we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:
Verify that
Therefore, the component form of this vector is
a)
b) See interpretation below
Step-by-step explanation:
a)
The motion of both balls is a free-fall motion: it means that the ball is acted upon the force of gravity only.
Therefore, this means that the motion of the ball is a uniformly accelerated motion, with constant acceleration equal to the acceleration of gravity:
in the downward direction.
For the ball dropped from the initial height of , the height at time t is given by
(1)
The ball which is thrown upward from the ground instead is fired with an initial vertical velocity , and its starting height is zero, so its position at time t is given by
(2)
Therefore, the polynomial that represents the distance between the two balls is:
b)
Now we interpret this polynomial, which is:
which represents the distance between the two balls at time t.
The interpretation of the two terms is the following:
- The constant term, , is the initial distance between the two balls, at time t=0 (in fact, the first ball is still at the top of the building, while the second ball is on the ground). For this problem,
- The coefficient of the linear term, , is the initial velocity of the second ball; this terms tells us that the distance between the two balls decreases every second by
feet.