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
It hits the ground at a horizontal distance $1.6 \,m$ from the edge of the table
The speed with which it hits the ground is $4.0\, m/second$
Height of the table is $0.8 \,m$
Both (a) and (c)
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
Vertical component of velocity of ball at point $P$
${v_V} = 0 + gt = 10 \times 0.4 = 4\,m/s$
Horizontal component of velocity = initial velocity
$ \Rightarrow {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 $\tan \theta = \frac{{{v_V}}}{{{v_H}}} = \frac{4}{4} = 1$ $⇒$ $\theta = 45^\circ $
It means the ball hits the ground at an angle of $45^\circ $ to the horizontal.
Height of the table $h = \frac{1}{2}g{t^2} = \frac{1}{2} \times 10 \times {(0.4)^2} = 0.8\,m$
Horizontal distance travelled by the ball from the edge of table $h = ut = 4 \times 0.4 = 1.6\,m$
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