Question

How long does it take a plane, travelling at a constant speed of 110 m/s, to fly once around a circle which radius is 2850 m? A driver of mass 50 kg jumps off a 6 meters high cliff. What is the change in her potential energy at the end of the fall? How fast does the go as the reactors the water?

Answer 1

Explanation:

It is given that,

Speed of the plane, v = 110 m/s

Radius of circle, r = 2850 m

(1) Let t is the time taken by a plane. Speed of the plane is given by :

$v=\dfrac{d}{t}=\dfrac{2\pi r}{t}$

$t=\dfrac{2\pi r}{v}$

$t=\dfrac{2\pi \times 2850}{110}$

t = 162.79 s

(2) Mass of a driver, m = 50 kg

Height, h = 6 m

As the driver reaches ground, its potential energy point to zero. So, the change in potential energy is given by :

$\Delta PE=PE_f-PE_i$

$\Delta PE=0-mgh$

$\Delta PE=-50\times 9.8\times 6$

$\Delta PE=-2940\ J$

So, the change in potential energy is 2940 joules.

Let v is the speed. As the driver reaches water surface, its potential energy is converted to kinetic energy as :

$\dfrac{1}{2}mv^2=PE$

$v=\sqrt{\dfrac{2\times PE}{m}}$

$v=\sqrt{\dfrac{2\times 2940}{50}}$

v = 10.84 m/s

So, the speed of the reactors the water is 10.84 m/s. Hence, this is the required solution.