Question

If a 20-kg object dropped in air has a terminal speed of 60 m/s, what was its acceleration at 30 m/s

Answer 1

Answer:

a = 7.35 m/s²

Explanation:

Given that,

Mass of a object, m = 20 kg

The terminal speed of the object, $v_t=60\ m/s$

We need to find its acceleration at 30 m/s.

It is a case on Newton's second law of motion. Its mathematical form can be given by :

$mg-F_D=ma$

Here, $F_D$ is the Drag force, $F_D=kv_t^2$

Putting all the values,

$mg-kv_t^2=ma$ ....(1)

Here, a = 0 Firstly we find the value of k (constant)

$k=\dfrac{mg}{v_t^2}\\\\k=\dfrac{20\times 9.8}{60^2}\\\\k=0.0545$

Now, put the value of k in equation (1) and here put v = 30 m/s

$a=\dfrac{mg-kv_t}{m}\\\\a=\dfrac{20(9.8)-0.0544\times 30^2}{20}\\\\a=7.35\ m/s^2$

So, its acceleration at 30 m/s is 7.35 m/s².