Question

(a) A projectile of mass 50 kg is shot vertically upwards with a velocity 100 m/s. after 5 sec the projectile explodes into two fragments, one of which (mass 20 kg) travels vertically up with a velocity of 150 m/s. What will be the velocity the other fragment at this moment ? (g = 9.8m/s2 )

Answer 1

Answer:

-15 m/s

Explanation:

$\red{\boxed{\rm Solution}}$

Initial mass of the body = 50 kg [Before breaking in fragments]

Intial velocity of the body = 100 m/s [Before breaking in fragments]

Applying the equations of motion on the body before 5 sec, i.e before breaking into fragments

u = 100 m/s

a = -g

t = 5 sec

v = ?

Applying first equation of motion, i.e v = u + at to find the value of final velocity (v)

v = 100 - 5g

v = 100 - 5(9.8)

v = 100 - 49

v = 51 m/s

Given that,

The 50 kg body breaks into two fragments, mass of one of the fragment is 20 kg, then the mass of the other fragment would be 30 kg.

Velocity of the 20 kg fragment = 150 m/s

Let the velocity of the 30 kg fragment be v

We know that momentum = mass of the body x velocity of the body

Applying the above formula to find the momentum of both the fragments as well as the 50 kg body before breaking into fragments,

Momentum of 50 kg at the instant where it breaks into fragments = 50 x (Velocity of the 50 kg body at that instant) = 50 x 51 = 2550 kg m/s

Momentum of 20 kg fragment = 20 x 150 = 3,000 kg m/s

Momentum of 30 kg fragment = 30 x v = 30v kg m/s

According to conservation of momentum,

The momentum of 50 kg body at which it breaks into 20 kg and 30 kg is equal to the sum of the momentum of 20 kg fragment and 30 kg fragment.

According to the above statement,

2550 = 3000 + 30v

2500 - 3000 = 30v

-450 = 30v

v = -450/30 = -15 m/s

$\boxed{\rm Velocity \: of \: the \: second \: fragment \: = \: -15 \: m/d}$

Here negative sign indicates that when the 50 kg body breaks into 20 kg and 30 kg fragments, the 20 kg fragment's velocity vector is in the same direction as the 50 kg body's velocity vector whereas the velocity vector of the 30 kg fragment is in the opposite direction as the velocity vector of the 50 kg body

Answer 2

Answer :-

-15m/s

Explanation :-

Given :

• Mass of the projectile,m = 50kg

• Initial velocity,u = 100m/s

• Time taken,t = 5s

• Mass of the first other fragment,m_2 = 20kg

• Velocity of the first fragment,u_1 = 150m/s

• Gravitational acceleration,g = 10m/s^2

Mass of the second fragment,m_2 = Total mass - First fragment mass

= (50 - 20) kg

= 30kg

To Find :

• Velocity of the other/second fragment,v_2 = ?

Solution :

Question says that a projectile was shotted which further exploded into two different fragment.

Let’s find out the velocity of the projectile after 5s by first equation of motion,

Note :-

The acceleration is negative when going up because the speed is decreasing.

$\sf{}:\implies v=u+at$           Here,a is same as g.

$\sf{}:\implies v=100-9.8\times 5$

$\sf{}:\implies v=100-49$

$\sf{}\therefore v=51m/s$

Therefore,final velocity of the projectlie is 51m/s

Now,we can the velocity of the second fragment.

According to the conversation law of momentum,initial momentum = final momentum

Initial momentum = Final momentum

$\sf{}:\implies mv =m_1v_1+m_2v_2$

$\sf{}:\implies 50kg\times 51m/s =20kg\times 150m/s+30v_2$

$\sf{}:\implies 2550kg\ m/s =3000kg\ m/s+30v_2$

$\sf{}:\implies -450kg\ m/s=30v_2$

$\sf{}:\implies -\dfrac{450kg\ m/s}{30}=v_2$

$\sf{}\therefore v_2=-15m/s$

Here,negative sign denotes that other fragment moved in a opposite direction.

Therefore,velocity of the other fragment is equal to -15m/s