A car starts from rest and accelerates at 5 m/s 2 . At t = 4 s , a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s ? (Take g = 10 m/s 2 ) [2021]

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Solution

Q.
A car starts from rest and accelerates at $5 {m/s}^{2}$ . At $t = 4 s$ , a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t = 6 s$ (Take $g = 10 {m/s}^{2}$ ) [2021]

1 $20 \sqrt{2} m/s, 10 {m/s}^{2}$

2 $20 m/s, 5 {m/s}^{2}$

3 $20 m/s, 0$

4 $20 \sqrt{2} m/s, 0$

Ans.
(1)

Given : $u_{x} = 0,$ $a_{x} = 5 {m/s}^{2}$

At $t = 4 s$ ball is dropped $a_{y} = g = 10 {m/s}^{2}$

Let $v_{x}$ is the velocity of ball at the time $t = 4 s.$

$v_{x} = u_{x} + a_{x} t = 0 + 5 \times 4 = 20 m/s$

$v_{y}$ is the velocity of ball after leaving at $t = 6 s$

$v_{y} = u_{y} + a_{y} t' = 0 + g \times 2 = 20 m/s$

Resultant velocity of ball at $t = 6 s$

$v = \sqrt{v_{x}^{2} + v_{y}^{2}} = \sqrt{20^{2} + 20^{2}}$

$\Rightarrow v = 20 \sqrt{2} m/s$

Acceleration of the ball will be due to gravity i.e., $a = 10 {m/s}^{2}$

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