Velocity and Time

A stone is dropped from the edge of a roof, and hits the ground with a velocity of -180 feet per second. How high (in feet) is t

Neko [114]

Answer:

d = 506.25 ft

Explanation:

As we know by kinematics that

$v_f^2 - v_i^2 = 2 a d$

here we know that initially the stone is dropped from rest from the edge of the roof

so here initial speed will be zero

now we have

$v_i = 0$

also the acceleration of the stone is due to gravity which is given as

$g = 32 ft/s^2$

now we have

$v_f = 180 ft/s$

so from above equation

$180^2 - 0 = 2(32)d$

$d = 506.25 ft$

6 0

3 years ago

An oscillator consists of a block attached to a spring (k = 427 N/m). At some time t, the position (measured from the system's e

White raven [17]

Answer:

a) 4.49Hz

b) 0.536kg

c) 2.57s

Explanation:

This problem can be solved by using the equation for he position and velocity of an object in a mass-string system:

$x=Acos(\omega t)\\\\v=-\omega Asin(\omega t)\\\\a=-\omega^2Acos(\omega t)$

for some time t you have:

x=0.134m

v=-12.1m/s

a=-107m/s^2

If you divide the first equation and the third equation, you can calculate w:

$\frac{x}{a}=\frac{Acos(\omega t)}{-\omega^2 Acos(\omega t)}\\\\\omega=\sqrt{-\frac{a}{x}}=\sqrt{-\frac{-107m/s^2}{0.134m}}=28.25\frac{rad}{s}$

with this value you can compute the frequency:

a)

$f=\frac{\omega}{2\pi}=\frac{28.25rad/s}{2\pi}=4.49Hz$

b)

the mass of the block is given by the formula:

$f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}\\\\m=\frac{k}{4\pi^2f^2}=\frac{427N/m}{(4\pi^2)(4.49Hz)^2}=0.536kg$

c) to find the amplitude of the motion you need to know the time t. This can computed by dividing the equation for v with the equation for x and taking the arctan:

$\frac{v}{x}=-\omega tan(\omega t)\\\\t=\frac{1}{\omega}arctan(-\frac{v}{x\omega })=\frac{1}{28.25rad/s}arctan(-\frac{-12.1m/s}{(0.134m)(28.25rad/s)})=2.57s$

Finally, the amplitude is:

$x=Acos(\omega t)\\\\A=\frac{0.134m}{cos(28.25rad/s*2.57s )}=0.45m$

5 0

3 years ago

6.All wheelchairs may be secured so that the user is facing the curb side of the vehicle.

Nataly_w [17]

All wheelchairs may be secured so that the user is facing the curb side of the vehicle is true. The answer is letter A. It provides a unique 180 degree powered rotation which makes it possible to raise, lower and rotate fully.

6 0

3 years ago

Two forces F1 = -7.90i + 5.40j and F2 = 9.00i + 7.60j are acting on an object with a mass of m = 6.30 kg. The forces are measure

IceJOKER [234]

Answer:

Propotionality is important

Explanation:

7 0

2 years ago

What is the meaning of joule

SOVA2 [1]

A joule is a unit of energy.