Question

a body is thrown vertically up from top of a building with a velocity of 10 metre per second it reaches the ground in 5 seconds find height of the building and the velocity with which the body reaches the ground ​

Answer 1

Given :-

▪ A body is thrown vertically up from top of a building with a velocity of u = 10 m/s. It reaches the ground in time T = 5 s.

To Find :-

▪ Height of the building and the velocity with which the body was thrown.

Solution :-

Taking g = 10 m/s² , Let's find the time taken by the ball to reach the maximum height ( i.e., point at which the velocity becomes zero )

⇒ v = u + at

⇒ 0 = 10 - 10t

⇒ 10t = 10

⇒ t = 1 s

Also, The body would take 2 seconds to reach the position at which it was thrown (i.e., top of the building)

So, Time taken by the body to travel the height of the building is (5 - 2) = 3 seconds with initial velocity of u = 10 m/s²

Now, Lets us find the Height of the building,

we have

• u = -10 m/s²
• g = -10 m/s²
• t = 3 s

Using second equation of motion,

⇒ h = ut + 1/2 at²

⇒ h = 10×3 + 1/2 × 10 × 3²

⇒ h = 30 + 5×9

⇒ h = 30 + 45

⇒ h = 75 m

Now, Let's find the velocity, which can be calculated as,

⇒ v = u + at

⇒ v = 10 + 10×3

⇒ v = 10 + 30

⇒ v = 40 m/s

Hence,

• Height of building = 75 m
• Velocity of body at the surface = 40 m/s

Answer 2

Given:-

• A body is thrown vertically up from top of a building with a velocity of 10 metre per second it reaches the ground in 5 seconds.

To find:-

• height of the building and the velocity with which the body reaches the ground.

Solution :-

When it goes up,

↠ v² = u² - 2as

↠ 0 = (10)² - 2 × 10 × s

↠ 0 = 100 - 20s

↠ - 100 = - 20s

↠ s = 5m

v = u - at [ thrown vertically which is opposite direction ]

⇢ u = at [ v = 0 ]

⇢ 10 = 10t

⇢ t = 1s

So, body would take 2 seconds to reach the height,

Time = 5 - 2 = 3s

⇢v = u + at

⇢v = 10 + 10 × 3

⇢v = 10 + 30

⇢v = 40m/s

So the body reaches in 5 - 1 = 4 s

as we know that,

↣ S = ut + 1/2at²

↣ s = 0 +1/2 × 10 × (4)²

↣ s = 1/2 × 10 × 16

↣ s = 80m

↣ So the height of building is 80 - 5 = 75m.

Hence,

• Velocity of body at surface = 40m/s.
• Height of building = 75m.