Question

Determine the initial velocity of a marble that lands 1.8m away from a tabletop that is 0.8m from the ground.

Acceleration due to gravity = 9.85
0 2.25 m/s
2.6 m/s
0 1.8 m/s
4.5 m/s

Answer 1

4.5 m/s

Step-by-step explanation:

`s_x` = Horizontal displacement = 1.8 m

`s_y` = Vertical displacement = 0.8 m

`u_x` = Horizontal velocity

g = Acceleration due to gravity =
`9.81\ \text{m/s}^2`

t = Time taken to fall down

`s_y=u_yt+(1)/(2)gt^2\\\Rightarrow 0.8=0+(1)/(2)* 9.8* t^2\\\Rightarrow t=\sqrt{(2* 0.8)/(9.8)}\\\Rightarrow t=0.4\ \text{s}`

`s_x=u_xt+(1)/(2)a_xt^2\\\Rightarrow 1.8=u_x* 0.4+0\\\Rightarrow u_x=(1.8)/(0.4)\\\Rightarrow u_x=4.5\ \text{m/s}`

The initial velocity of the marble is 4.5 m/s.