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2 years ago

Gretchen runs the first 4.0 km of a race at 5.0 m/s. Then a stiff wind comes up, so she runs the last 1.0 km at only 4.0 m/s.

Physics

1 answer:

KIM [24]2 years ago

7 0

Answer:

The velocity is $v = 4.76 \ m/s$

Explanation:

From the question we are told that

The first distance is $d_1 = 4.0 \ km = 4000 \ m$

The first speed is $v_1 = 5.0 \ m/s$

The second distance is $d_2 = 1.0 \ km = 1000 \ m$

The second speed is $v_2 = 4.0 \ m/s$

Generally the time taken for first distance is

$t_1 = \frac{d_1 }{v_1 }$

$t_1 = \frac{4000}{5}$

$t_1 = 800 \ s$

The time taken for second distance is

$t_1 = \frac{d_2 }{v_2 }$

$t_1 = \frac{1000}{4}$

$t_1 = 250 \ s$

The total time is mathematically represented as

$t = t_1 + t_2$

=> $t = 800 + 250$

=> $t = 1050 \ s$

Generally the constant velocity that would let her finish at the same time is mathematically represented as

$v = \frac{d_1 + d_2}{t }$

=> $v = \frac{4000 + 1000}{1050 }$

=> $v = 4.76 \ m/s$

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A worker kicks a flat object lying on a roof. The object slides up the incline 10.0 m to the apex of the roof, and flies off the

11111nata11111 [884]

Answer:15.20 m

Explanation:

Given

initial velocity $(v_i)=15 m/s$

inclined length=10 m

$\mu _k=0.435$

inclination $\theta =43.5^{\circ}$

$F_{net}=f_r+mg\sin \theta$

$a_{net}=\mu _kg\cos \theta +g\sin \theta$

$a_{net}=0.435\times 9.8\times \cos 43.5+9.8\times \sin 43.5$

$a_{net}=3.09+6.74=9.83 m/s^2$

$v^2-u^2=2as$

$v^2=15^2-2\times (9.83)10$

$v=5.31 m/s$

So Particle launches with a speed of 5.31 m/s at an angle of \theta $=43.5$

$h_{max}=\frac{u^2\sin^2\theta }{2g}$

$h_{max}=\frac{(5.31)^2\sin ^2(43.5)}{2\times 9.81}$

$h_{max}=0.679$

Total height raised is $0.679+\frac{10}{\sin 43.5} =15.20 m$

6 0

2 years ago

A glider is gliding through the air at a height of 416 meters with a speed of 45.2 m/s. The glider dives to a height of 278 mete

Verdich [7]

Answer:

<em>The glider's new speed is 68.90 m/s</em>

Explanation:

<u>Principle Of Conservation Of Mechanical Energy</u>

The mechanical energy of a system is the sum of its kinetic and potential energy. When the only potential energy considered in the system is related to the height of an object, then it's called the gravitational potential energy. The kinetic energy of an object of mass m and speed v is

$\displaystyle K=\frac{1}{2}mv^2$

The gravitational potential energy when it's at a height h from the zero reference is

$U=mgh$

The total mechanical energy is

$M=K+U$

$\displaystyle M=\frac{1}{2}mv^2+mgh$

The principle of conservation of mechanical energy states the total energy is constant while no external force is applied to the system. One example of a non-conservative system happens when friction is considered since part of the energy is lost in its thermal manifestation.

The initial conditions of the problem state that our glider is glides at 416 meters with a speed of 45.2 m/s. The initial mechanical energy is

$\displaystyle M_1=\frac{1}{2}m(45.2)v_o^2+m(9.8)(416)$