A ball is rolled off the edge of a horizontal table at a speed of `4 m//"second"`. It hits the ground after 0.4 second . Which statement given below is true

Options

A. It hits the ground at a horizontal distance 1.6 m from the edge of the table
B. The speed with which it hits the ground is `4.0 ms^(-1)`
C. Height of the table 1m
D. It hits the ground at an angle of `60^(@)` to the horizontal

Answer

A

Explanation

Vertical component of velocity of ball at point P
`u_(V) = 0 + g t = 10 xx 0.4 = 4 ms^(-1)`
Horizontal component of velocity = initial velocity
`rArr v_(H) = 4 m//s`

So, the speed with which it hits the ground
`v = sqrt(v_(H)^(2) +v_(V)^(2)) = 4 sqrt(2)m//s`
and `tan theta = (v_(V))/(v_(H)) = (4)/(4) = 1 rArr theta = 45^(@)`
If means the ball hits the ground at an angle of `45^(@)` to the horizontal. Height of the table `h = (1)/(2)g t^(2) = (1)/(2) xx 10 xx (0.4)^(2) = 0.8m`
Horizontal distance travelled by the ball from the edge of table `h = ut = 4 xx 0.4 = 1.6 m`