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.

$v_V$ = 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 and tan $\theta =\frac{v_V}{v_H}=\frac{4}{4}=1\Rightarrow \theta ={45}^o$

It means the ball hits the ground at an angle of ${45}^o$ 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