QJEEM23Ph8e60: JEE Main 2023 Physics - Class 11 JEEM23Ph8e60 Solution: A ball is thrown vertically upward with an initial velocity of…

To solve this problem, we can use the following equation of motion for the vertical velocity at any given time $t$ :

$v = u - gt$

Where:

- $v$ is the final velocity at time $t$

- $u$ is the initial velocity (150 m/s)

- $g$ is the acceleration due to gravity (10 m/s²)

- $t$ is the time in seconds

First, we need to find the velocities at $t = 3 \mathrm{~s}$ and $t = 5 \mathrm{~s}$ .

For $t = 3 \mathrm{~s}$ :

$v_3 = 150 - (10)(3) = 150 - 30 = 120 \mathrm{~m} / \mathrm{s}$

For $t = 5 \mathrm{~s}$ :

$v_5 = 150 - (10)(5) = 150 - 50 = 100 \mathrm{~m} / \mathrm{s}$

Now we need to find the ratio of these velocities:

$\frac{v_3}{v_5} = \frac{120}{100} = \frac{6}{5} = \frac{x + 1}{x}$

Next, we can set up an equation to find the value of $x$ :

$\frac{6}{5} = \frac{x + 1}{x}$

Now, we can solve for $x$ :

$6x = 5(x + 1)$

$6x = 5x + 5$

$x = 5$

The value of $x$ is 5.