Question

A ball is projected vertically upwardsits speed at half of maximum height is 30m/s maximum height attained by the ball is

Answer 1

Answer:

Max Height = 90 m

Vh = V/√2

Explanation:

A ball is projected vertically upwardsits speed at half of maximum height is 30m/s maximum height attained by the ball is

Let Say Ball is thrown With Velocity V

Speed at Max height = 0

V² - U² = 2aS

=> 0² -V² = 2(-g)H

=> V² = 2gH

=> H = V²/2g

Max Height = H

Velocity at H/2  = Vh

Vh² - U² = 2a(H/2)

=> Vh² - V² = -2gH/2

=> Vh² - V² = -V²/2

=> Vh² = V²/2

=> Vh = V/√2

Speed at half of max height would be 1/√2 times of Projected Speed

Vh = 30 m

V = 30√2

H = V²/2g   = (30√2)²/2*10 = 90 m

Max Height = 90 m

Answer 2

Let maximum height attained by ball is H.

the ball is projected vertically upwards and its speed at half of maximum height (i.e., H/2) is 30m/s.

let velocity of ball at the height H/2 from the ground = initial velocity of ball , u = 30m/s

we know, velocity at maximum height becomes zero.

so, final velocity of ball , v = velocity at maximum height = 0

now using formula, v² = u² + 2as

here , v = 0, u = 30 , a = -g = -10m/s² and s = H/2

so, 0² = 30² + 2(-10) × H/2

or, H = 90 m

hence, maximum height attained by ball is 90m