Question

A stone of mass 500 g is thrown vertically upwards with a velocity of 15 m/s. Calculate:

1. the potential energy at the greatest height,
2. the kinetic energy on reaching the ground, and
3. the total energy at its half-way point.

Answer 1

(a) Mass of stone m = 500 g = `500/1000 = 1/2 kg`

v = 0

u = 15 m/s

∴ v² - u² = 2gh

0 – 15 × 15 = 2gh

∴ gh = `(-225)/2`

10 h = `(-225)/2 or h = (-225)/(20) m`

A negative sign shows the stone is moving upward.

∴ Potential Energy = mgh

= `1/2 xx 10 xx 225/20`

= 56.25 J

(b) On the way back

u = 0, h = `225/20  m`, v = ?

v² - u² = 2gh

∴ v² - 0 = `2 × 10 × 225/20`

∴ v² - 0 = 225

∴ v = `sqrt225`

∴ v = 15 ms^-1

K.E on reaching ground = `1/2 mv^2`

= `1/2 xx 1/2 xx 15 xx 15`

= 56.25 J

(c) Total energy at halfway point = mgh

= `1/2 xx 10 xx 225/20`

= 56.25 J