Question

A ball is rolled off the edge of a horizontal table at a speed of 4 ms^-1. It hits the ground after 0.4 s.
Which statement given below is true?

Moderate

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 is 1m.
D

It hits the ground at an angle of 60° to the horizontal.

Solution

Vertical component of velocity of ball at point P.
$u_{V} = 0 + g t$
= 10 X 0.4 = 4ms-1
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 $\tan θ = \frac{v_{V}}{v_{H}} = \frac{4}{4} = 1 \Rightarrow θ = 45 °$
It means the ball hits the ground at an angle of 45⁰ 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 $h = u t = 4 \times 0.4 = 1.6 m$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

SCAN ME