Question

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

• 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 m/second
• C. Height of the table is 0.8 m
• D. It hits the ground at an angle of 60^o to the horizontal

Answer 1

Answer: (A), (C)

The correct options are
A It hits the ground at a horizontal distance 1.6 m from the edge of the table
C Height of the table is 0.8 m

Vertical component of velocity of ball at point P
$v_0+gt=10\times 0.4=4m/s$
Horizontal component of velocity = initial velocity
$\Rightarrow v_H=4m/s$

So the speed with which it hits the ground
$v=\sqrt{v_H^2+v_v^2}=4\sqrt{2}m/s$
$andtan\theta =\frac{v_V}{v_H}=\frac{4}{4}=1\Rightarrow \theta ={45}^{\circ }$
It means the ball hits the ground at an angle of ${45}^{\circ }$ to the horizontal.
Height of the table
$h=\frac{1}{2}g{t}^2=\frac{1}{2}\times 10\times (0.4{)}^2=0.8m$
Horizontal distance travelled by the ball from the edge of table $h=ut=4\times 0.4=1.6m$