Question

An object is thrown vertically upwards and rises to a height of 80 m. Calculate the velocity with which the object was thrown upwards? G = 10m/s²​

Answer 1

Answer :

Maximum height attained by object = 80m

Acceleration due to gravity = 10m/s²

We have to find velocity with which the object was thrown upwars$.$

1) For a body falling under the action of gravity, g is taken positive.

2) For a body thrown vertically upward, g is taken negative.

➤ For a body thrown vertically up with initial velocity u,

• Max. height reached, h = u²/2g
• Time of ascent = u/g
• Total time of flight = 2u/g
• Velocity of fall at the point of projection = u

➝ v² - u² = 2gH

At maximum height, v = 0

➝ 0² - u² = 2(-g)H

➝ H = u²/2g

➝ 80 = u²/2(10)

➝ u² = 80×20

➝ u = √1600

➝ u = 40 m/s

Answer 2

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• Height = 80 m

• Final Velocity ( v ) = 0 m/s

• Gravity ( g ) = - 10 m/s²

• Initial Velocity ( u ) = ?

⠀

$\underline{\bigstar\:\textsf{Using Third Equation of Gravity :}}$

$:\implies\sf (v)^2-(u)^2=2gh\\\\\\:\implies\sf (0)^2-(u)^2=2 \times (-10) \times 80\\\\\\:\implies\sf -(u)^2= - 1600\\\\\\:\implies\sf (u)^2= 1600\\\\\\:\implies\sf u = \sqrt{1600}\\\\\\:\implies\underline{\boxed{\sf u = 40\:m/s}}$

⠀