Physics, 02.03.2020 17:46, cl6205071

(a) A daredevil is attempting to jump his motorcycle over a line of buses parked end to end by driving up a 32º ramp at a speed of 40.0 m/s (144 km/h) . How many buses can he clear if the top of the takeoff ramp is at the same height as the bus tops and the buses are 20.0 m long? (b) Discuss what your answer implies about the margin of error in this act—that is, consider how much greater the range is than the horizontal distance he must travel to miss the end of the last bus. (Neglect air resistance.)

Answers: 2

Show answers

Answers

answered: zmeister

a) 7 buses

b) 6.8 m

Explanation:

The motion of the motorcycle is a projectile motion, so it consists of 2 independent motions:

- A uniform motion along the horizontal direction

- A uniformly accelerated motion along the vertical direction

The initial components of the velocity of the motorcycle are:

$v_x = u cos(32^{\circ})=(40.0)(cos 32^{\circ})=33.9 m/s\\v_y = u sin(32^{\circ})=(40.0)(sin 32^{\circ})=21.2 m/s$

The equation for the vertical motion of the motorcycle is

$y=h+u_y t - \frac{1}{2}gt^2$

where

y is the altitude at time t

h is the initial height

g=9.8 m/s^2 is the acceleration due to gravity

The bus top is at the same height of the initial ramp, so we have

y=h

And therefore, we can solve the equation for t, to find the time of flight:

$0=u_y t - \frac{1}{2}gt^2\\t(u_y-\frac{1}{2}gt)=0\\t=\frac{2u_y}{g}=\frac{2(21.2)}{9.8}=4.33 s$

Now we find what is the horizontal distance covered by the motorcycle in its jump, which is given by:

d=v_x t = (33.9)(4.33)=146.8 m

And since each bus has a length of L = 20.0 m, the number of buses that the motorcycle can clear with its jump is:

$n=\frac{d}{L}=\frac{146.8}{20}=7.34$

So, 7 buses.

In the previous problem, we saw that the total range of the motion of the motorcycle is

d=146.8 m

And we said that this corresponds to 7 buses.

Each bus has a length of

L = 20 m

So, the total length of 7 buses is

L' = 7L=7(20)=140 m

Therefore, the range of the motorcycle is greater than the length of the buses by:

$\Delta x = d-L'=146.8-140 = 6.8 m$

which means he will miss the last bus by 6.8 meters.

answered: Guest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

answered: Guest

Wooden , walls ,doors ,support

Other questions on the subject: Physics

Physics, 22.06.2019 05:30, emmeaw245

The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5. what is the specific heat ratio? show the math steps .

Answers: 3

continue

Physics, 22.06.2019 19:40, rileybaby34

Uranium has two naturally occurring isotopes. 238u has a natural abundance of 99.3% and 235u has an abundance of 0.7%. it is the rarer 235u that is needed for nuclear reactors. the isotopes are separated by forming uranium hexafluoride uf6, which is a gas, then allowing it to diffuse through a series of porous membranes. 235uf6 has a slightly larger rms speed than 238uf6 and diffuses slightly faster. many repetitions of this procedure gradually separate the two isotopes. what is the ratio of the rms speed of 235uf6 to that of 238uf6? express your answer to five significant figures.

Answers: 3

continue

Physics, 22.06.2019 23:30, roman2328

When barack obama was running for president, at a campaign stop he tried to bowl, something he isn't very good at. the media loved it because he threw a gutter ball while they were all watching. this is an example of:

Answers: 2

continue

Physics, 23.06.2019 06:40, BobreyesV20

12. ritu obtained a distinct image of a distant tree on the screen with the of a concave mirror. to find the focal length of the mirror she has to measure the distance between: (a) mirror and the tree. (b) screen and the tree.(c) mirror and the screen. (d) mirror and tree as well as between screen and the tree.

Answers: 2

continue

Do you know the correct answer?

(a) A daredevil is attempting to jump his motorcycle over a line of buses parked end to end by drivi...