Question

it stone is dropped from a hill of height
18om Two seconds later another a stone
is dropped from
point p below the top of
the hill - If the 2 stones reach the ground simentously
height of P from ground is (g=10ms -2) .Please help me​

Answer 1

Answer :

Given -

• The height of the hill = 180 m.
• First stone is thrown from the top of the hill.
• Second stone is thrown from point P.
• Point P is below the top of the hill.
• The other stone is dropped after 2 seconds.
• g = 10 m/s².
• The 2 stones reach the ground simultaneously.

To Find -

• Height of P point.

Solution -

By Newton's second equation of motion :

⇒ s = ut + ½at²

⇒ 180 = 0*t + ½*10*t²

⇒ 180 = 0 + 5t²

⇒ 5t² = 180

⇒ t² = 180/5

⇒ t² = 36

⇒ t = √36

⇒ t = 6 seconds

As both of them (stones) reach the ground at the same time, the time taken to reach the ground for the second stone will be 4 seconds. [It was dropped 2 seconds later]

Now, Let us find the Height of point P -

⇒ s = ut + ½at²

⇒ s = 0*4 + ½*10*4²

⇒ s = 0 + 5*16

⇒ s = 5 × 16

⇒ s = 80 m

Hence, The Height of the Point P from the ground = 80 m.

Answer 2

Given , a stone is dropped from a hill of height 180 m. 2 sec later another stone is dropped from point p below the top of the hill. 2 stones reach the ground simultaneously i.e., at same time. We need to find the height of P ?

So here ,

Case -1 : For 1st stone

Height , s = 180 m

Initial velocity , u = 0 m/s

Acceleration due to gravity , g = 10 m/s²

Time , t = ?

use Second equation of motion

⇒ s = ut + 1/2gt²

⇒ 180 = 1/2*10*t²

⇒ 180 = 5t²

⇒ t² = 36

⇒ t = 6 sec

So the time needed for 1st stone to reach the ground is 6 sec.

Now both stones reaches the ground at same time. But 2nd stone started after 2 sec.

So the total time taken for 2nd stone is 6 - 2 = 4 sec

__________________________

Case 2 :- For 2nd stone

Time , t = 4 sec

Initial velocity , u = 0 m/s

Acceleration due to gravity , g = 10 m/s²

Distance , s = ? m

So use Second equation of motion.

⇒ s = ut + 1/2 at²

⇒ s = ut + 1/2 gt²

⇒ s = 0 * 2 + 1/2 * 10 * 4²

⇒ s = 80 m

So height of the P from ground is 80 meters.