Question

what is meant by free fall ? a ball is thrown vertically upward with a velocity of 49 m / s. calculate
1. the maximum height to which it reaches
2. the total time it takes to return to the surface of the earth g = 9.8 m /s2​

Answer 1

Answer:

1. Free fall :

A body is said to be in free fall, if it's falling from a height under the gravitational force only.

It means that, when an object is falling from a particular height, the force which will be acting on it should be only gravitational force.

2. Given that,

Initial velocity (u) = 0 m/s (as body is in rest.)

Final velocity (v) = 49 m/s

Acceleration due to gravity (g) = 9.8 m/s²

To find,

(i) the maximum height it reaches

(ii) the total time it takes to return to the surface of the earth.

(i) As we know,

There are three equations of motion, they are : -

(a) v = u + at

(b) s = ut + $\frac{1}{2}$ at²

(c) 2as = v² - u²

But we've to find the distance, so we can't use 1st equation of motion as there's no value of distance (s).

 We can't also use 2nd equation of motion, as we don't know the value of time.

We can use 3rd equation of motion, we'll use 3rd equation of motion.

By using 3rd equation of motion,

2as = v² - u²

2(9.8)s = (49)² - (0)²

19.6s = 2,401 - 0

19.6s = 2,401

s = $\frac{2,401}{19.6}$

s = $\frac{\cancel{2,401}}{\cancel{19.6}}$

$\boxed{\bold{s = 122.5\:m}}$

But what if we use the 2nd equation of motion to find the distance?

But we don't know the value of time (t). So, we are unable to reckon it.

(ii) By using 1 equation of motion,

v = u + at

49 = 0 + 9.8 * t

49 = 9.8t

$\frac{49}{9.8}$ = t

$\frac{\cancel{49}}{\cancel{9.8}}$ = t

5 s = t

$\boxed{\bold{Time\:(t)= 5\:seconds}}$

Answer 2

So,

When a body is falling from a height and the force acting on it is Gravitational force only. Then the body is said to be freely Falling or Free fall.

Now,

Given:-

=> Final Velocity = 49 m/s

=> Acceleration due to Gravity = 9.8 m/s^2

In order to find Height we will apply the Third Equation of Motion.

=> v^2 = u^2 + 2gh

=> (49)^2 = 0^2 + 2 x 9.8 x h

=> 49 x 49 = 19.6 h

=> 19.6 h = 49 x 49

=> h = 49 x 49/19.6

=> h = (49 x 2.5) m

$\bold{=> h = 122.5 m}$

Again,

In order to find time we will apply First Equation of Motion. However, we can solve it by using Second Equation of Motion also.

=> v = u + gt

=> 49 = 0 + 9.8 x t

=> t = 49/9.8

$\bold{=> t = 5 s}$

Hence,

=> The height achieved or reached by it = 122.5 m

=> Time taken to return = 5 s