If your mass is 63.7 kg, and you are standing 7.5 m away from a boulder with

Where is potential energy the greatest on a rollercoaster?

lidiya [134]

On a roller coaster, the greatest potential energy is at the highest point of the roller coaster

4 0

3 years ago

In a flying ski jump, the skier acquires a speed of 110 km/h by racing down a steep hill and then lifts off into the air from a

matrenka [14]

Answer:

Approximately $\displaystyle\rm \left[ \begin{array}{c}\rm191\; m\\\rm-191\; m\end{array}\right]$ .

Explanation:

Consider this $45^{\circ}$ slope and the trajectory of the skier in a cartesian plane. Since the problem is asking for the displacement vector relative to the point of "lift off", let that particular point be the origin $(0, 0)$ .

Assume that the skier is running in the positive x-direction. The line that represents the slope shall point downwards at $45^{\circ}$ to the x-axis. Since this slope is connected to the ramp, it should also go through the origin. Based on these conditions, this line should be represented as $y = -x$ .

Convert the initial speed of this diver to SI units:

$\displaystyle v = \rm 110\; km\cdot h^{-1} = 110 \times \frac{1}{3.6} = 30.556\; m\cdot s^{-1}$ .

The question assumes that the skier is in a free-fall motion. In other words, the skier travels with a constant horizontal velocity and accelerates downwards at $g$ ( $g \approx \rm -9.81\; m\cdot s^{-2}$ near the surface of the earth.) At $t$ seconds after the skier goes beyond the edge of the ramp, the position of the skier will be:

$x$ -coordinate: $30.556t$ meters (constant velocity;)
$y$ -coordinate: $\displaystyle -\frac{1}{2}g\cdot t^{2} = -\frac{9.81}{2}\cdot t^{2}$ meters (constant acceleration with an initial vertical velocity of zero.)

To eliminate $t$ from this expression, solve the equation between $t$ and $x$ for $t$ . That is: express $t$ as a function of $x$ .

$x = 30.556\;t\implies \displaystyle t = \frac{x}{30.556}$ .

Replace the $t$ in the equation of $y$ with this expression:

$\begin{aligned} y = &-\frac{9.81}{2}\cdot t^{2}\\ &= -\frac{9.81}{2} \cdot \left(\frac{x}{30.556}\right)^{2}\\&= -0.0052535\;x^{2}\end{aligned}$ .

Plot the two functions:

$y = -x$ ,
$\displaystyle y= -0.0052535\;x^{2}$ ,

and look for their intersection. Refer to the diagram attached.

Alternatively, equate the two expressions of $y$ (right-hand side of the equation, the part where $y$ is expressed as a function of $x$ .)

$-0.0052535\;x^{2} = -x$ ,

$\implies x = 190.35$ .

The value of $y$ can be found by evaluating either equation at this particular $x$ -value: $x = 190.35$ .

$y = -190.35$ .

The position vector of a point $(x, y)$ on a cartesian plane is $\displaystyle \left[\begin{array}{l}x \\ y\end{array}\right]$ . The coordinates of this skier is approximately $(190.35, -190.35)$ . The position vector of this skier will be $\displaystyle\rm \left[ \begin{array}{c}\rm191\\\rm-191\end{array}\right]$ . Keep in mind that both numbers in this vectors are in meters.

4 0

3 years ago

Ice-skater slides toward a sled sitting on the ice and hits it. The skater exerts a 12.6 N force on the sled at an angle of 15.3

RideAnS [48]

Answer:

Expression of work done is

$W = Fd cos\theta$

Work done to move the sled is given as 187.2 J

Explanation:

As we know that the formula of work done is given as

$W = Fd cos\theta$

here we know that

F = 12.6 N

d = 15.4 m

$\theta = 15.3 degree$

so we will have

$W = 12.6 \times 15.4 cos15.3$

$W = 187.2 J$

5 0

3 years ago

1. What is the total distance traveled?<br> A 3.0m <br> B 4.0m <br> C 5.0m <br> D 6.0m

Ostrovityanka [42]

Answer:

c

Explanation:

7 0

2 years ago

Which of the following is true about light waves and sound waves? A. Sound waves can move at different speeds, but light waves a

vivado [14]

Answer:

C

Explanation:

Sound waves speed up noticeably when moving through a solid or liquid, because all it is is just particles colliding; and particles are way closer together with those states of matter.

The speed of light can change when moving through different substances, but this is dependent on complicated factors such as frequency, polarization, intensity, et. cetera

The important part is that it does change speed, so your answer is C.

Hope this helps!

3 0

3 years ago