Question

The man releases a ball from the roof of a house with a horizontal velocity Uo 10.4 m/s so that it just clears the corner B and reaches point C as shown. Determine the distance s in metres​

Answer 1

Answer:

2.5 m

Explanation:

The man releases a ball from the roof of a house with a horizontal velocity Uo 10.4 m/s so that it just clears the corner B and reaches point C as shown. Determine the distance s in metres​

Man releases ball from a height of  4 + 3 + 1 = 8m

When horizontal Distance of 6 m is covered then 4 m  Vertical Distance is covered

V₀  = 10.4 m/s  ( horizontal Velocity)

Vertical Velocity = 0 m/s

Let say in time T₁ it reaches point B

Vertical Distance = 0*T + (1/2)gT₁² = 4

=> T₁² = 8/g

Horizontal Distance = V₀ * T₁ = 6

=> 10.4 *  T₁ = 6

=> T₁ = 6 /10.4 = 3/5.2

8/g = (3/5.2)²

=> g = 8 * 5.2²/3

Let say at T₂ it reaches point C

Horizontal Distance = 10.4 * T₂

Vertical Distance = (1/2)gT₂² = 8

=> T₂² = 16/g

=> T₂² = 2 * (8/g)

=> T₂² = 2 *  (3/5.2)²

=>  T₂ = √2 * 3/5.2

Horizontal Distance =  10.4 * T₂ = 10.4 * √2 * 3/5.2  = 6√2  = 8.5 m

s = 8.5 - 6 = 2.5 m