Una roca de 32 kg se encuentra en caída libre y cuando le faltan 18 m para llegar al piso su velocidad es de 49 m/s
a)¿Desde que altura cayó?
b)¿Con que velocidad llegará al piso?

1) The height the rock fell from = 140.5m

2) velocity = 52.48m/s

Explanation:

Question:

A 32 kg rock is in free fall and when it is 18 m to reach the ground its speed is 49 m / s.

a) From what height did you fall?

b) With what speed will it reach the floor?

Solution:

See attachment for the diagram

m = 32kg

Velocity at height 18m before reaching ground = 49m/s

1) The potential energy (P.E) when the ball is at rest on the top = mass × acceleration due to gravity × height

P.E = mgh

h = ?

Let acceleration due to gravity (g) = 9.8m/s^2

P.E = 32 × 9.8 × h

P.E = 313.6h

Since the potential energy gets converted into kinetic energy at the same rate when the rock is in motion,

the kinetic energy when the ball will be 18m before hitting the ground at velocity 49m/s:

Kinetic energy (K.E) = 1/2mv^2

K.E = 1/2× 32 × (49)^2

K.E = 38416Joules

P.E = K.E

78.4h = 38416

h = 38416/313.6

h = 122.5m

The height the rock fell from (H) = h + 18 = 122.5+18

The height the rock fell from (H) = 140.5m

2) The speed the rock will reach the ground = maximum velocity

P.E = mgH

P.E = 32×9.8×140.5

P.E = 44060.8Joules

K.E = 1/2mv^2

K.E = 1/2 × 32 ×v^2

K.E = 16×v^2

P.E =K.E

44060.8 = 16×v^2

v^2 = (44060.8)/16

v^2 = 2753.8

v = √2753.8

v = 52.48m/s

The speed the rock will reach the ground = 52.48m/s

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