A small ball is thrown at an angle `45^(@)` to the horizontal with an initial velocity of `2 sqrt2m//s.` The magnitude of mean velocity averaged over the first 2 s is [take, acceleration due to gravity, `g = 10 m//s ^(2)]`

Options

A. `7.0 m//s`
B. `8.2m//s`
C. `7.8 m//s`
D. `9 m//s `

Answer

B

Explanation

Horizontal displacement in 2 seconds,
`x = mu_(x) x t = 2 sqrt2 cos 45^(@) xx 2=4 m`
Vertical displacement in 2 seconds,
`y = mu_(yt)+ 1/2 a _(yt) 2`
`=2 sqrt2 sin 45^(@) xx 2 -1/2 xx 10 xx4 =3-20= -16m`
Total displacement of particle in first 2 seconds
`= sqrt(x ^(2) + y ^(2)) = sqrt(4 ^(2) + 16 ^(2))= 16.49m`
Average Velocity = `("Total displacement ")/("Total time")`
`= (16.49)/(2) = 8.24 ms ^(-1) ~~8.2ms^(-1)`