Question

A ball is rolled off the edge of a horizontal table at a speed of 4 m/s. It hits the ground after 0.4 second. Which statement given below is true(Take $g=10m/s^2$)

• 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 1.8 m
• D. It hits the ground at an angle of 60^o to the horizontal

Answer 1

The correct option is A It hits the ground at a horizontal distance 1.6 m from the edge of the table

Vertical component of velocity of ball at point P
$v_v$ = 0 + gt = 10 $\times$ 0.4 = 4 m/s
Horizontal component of velocity = inital velocity
$\Rightarrow$ $v_H$ = 4 m/s
So the speed with which it hits the ground
v = $\sqrt{({v_H}^2+{v_y}^2)}$ = 4$\sqrt{2}$ m/s
and tan $\theta$ = $\frac{v_V}{v_H}$ =$\frac{4}{4}$ = 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 $\times$ ${\left(0.4\right)}^2$ = 0.8m
Horizontal distance travelled by the ball from the edge of table h = ut = 4 $\times$ 0.4 = 1.6m