Question

An object is dropped without initial speed

from a height of 20 m above ground and falls
with a constant acceleration of 10 m.s-2.
a. How long does it take the object to
reach the ground?
b. What is its speed upon reaching
ground?

Answer 1

a. t = 2 s

b. vf = 20 m/s

Step-by-step explanation:

a.

We can the second equation of motion to find out the time to reach the ground:

`h = v_it + (1)/(2)at^2`

where,

h = height = 20 m

vi = initial velocity = 0 m/s

t = time taken to reach the ground = ?

a = acceleration = 10 m/s²

Therefore,

`20\ m = (0\ m/s)t+(1)/(2) (10\ m/s^2)t^2\\\\t^2 = (20\ m)/(5\ m/s^2)\\\\t = √(4\ s^2)`

t = 2 s

b.

Here, we will use the first equation of motion to find the final speed:

`v_f = v_i + at\\v_f = 0\ m/s + (10\ m/s^2)(2\ s)`

vf = 20 m/s