Aprojectile of mass 2 kg is fired with a speed of 20 m/s at an angle of 30° with respect to the horizontal. (a) calculate the initial total energy of the projectile given that the reference point of zero gravitational potential energy at the launch position. (b) calculate the kinetic energy at the highest vertical position of the projectile. (c) calculate the gravitational potential energy at the highest vertical position. (d) calculate the maximum height that the projectile reaches. compare this result by solving the same problem using your knowledge of projectile motion.

Explanation:

a ) Initial kinetic energy

1/2 mv²

= .5 x 2 x 20 x 20

= 400 J

Total energy = P E + KE

0 + 400 = 400 J

b )

Velocity at the highest point will be equal to horizontal component of initial velocity

= 20 cos 30

= 17.32 m/s

Kinetic energy at the highest point

= ,5 x 2 x 17.32²

= 299.98 J

c )

gravitational potential energy at the highest vertical position

= initial total energy - kinetic energy at the highest point

= 400 - 299.98

= 100 J

d )

PE = mgh

h = PE / mg

= 100 / 2 x 9.8

= 5.1 m

e ) height achieved by a projectile

= u²sin²θ / 2g

= 20 x 20 x sin²30 / 2 x 9.8

= 5.1 m

the Time frame of light traveling k from earth to sun is lower than that milky way galaxy.

Explanation: our solar system is a member of the milky way galaxy , the ages of these planets are measured with the way light travels. It takes more time for light to travel around the milky way and to the milky way galaxy than the the sun.