Question

A ball is thrown upwards from the foot of a tower. The ball crosses the top of tower twice after an interval of 4 seconds and the ball reaches ground after 8 seconds, then the height of tower is ______ m. (g = 10 m/s²)

Options

• 50

• 60

• 70

• 80

Answer 1

A ball is thrown upwards from the foot of a tower. The ball crosses the top of tower twice after an interval of 4 seconds and the ball reaches ground after 8 seconds, then the height of tower is 60 m. (g = 10 m/s²)

Explanation:

h = ut - `1/2`gt²

or gt² - 2ut + 2h = 0

t₁t₂ = `(2"h")/"g"` and

Let t₁ and t₂ are the roots of the above equation.

For any general quadratic equation ax² + bx + c = 0, which have the root x 

and y then (x + y) = `-"c"/"a"` product of root (xy) = `"b"/"a"`,

So, sum of roots

t₁ + t₂ = `(2"u")/"g"` = T   

∴ (t₁ - t₂)² = (t₁ + t₂)² - 4t₁t₂

16 = 64 - 4 × `(2"h")/"g"`

⇒ h = 60 m