A projectile of mass 3m is projected from ground with velocity 20root2 m/s at an angle 45°.at highest point it explodes into two peices. one of mass 2m and the other of mass m. mass 2m falls at a distance of 100m from point of projection towards right of point of projection. if the distance (in m) of second mass from point of projection where it strikes the ground is nx10, then n is (g=10m/s^2)

Let's break down the problem step by step to find the distance where the second mass strikes the ground.

Step 1: Analyzing the Projectile Motion

When the projectile reaches its highest point, it splits into two masses. The horizontal and vertical components of the initial velocity remain unchanged for both masses. The horizontal component is given by:

Horizontal Component: $V_{0x}=V_0\cdot \cos (\theta )$

Vertical Component: $V_{0y}=V_0\cdot \sin (\theta )$

Step 2: Finding Time of Flight

Since the projectile follows a parabolic path, the time of flight can be calculated using the vertical component of the velocity:

$t=\frac{2\cdot V_{0y}}{g}$

Step 3: Finding Horizontal Distance Traveled

For the mass of $2m$, the horizontal distance traveled ($d$) is given by:

$d=V_{0x}\cdot t$

Step 4: Finding Distance of the Second Mass

For the mass of $m$, the horizontal distance traveled would be twice the distance of the mass of $2m$ due to the same initial horizontal velocity. Therefore, the distance will be:

$2\cdot d=2\cdot V_{0x}\cdot t$

Substitute the values of $V_{0x}$ and $t$ to find the distance where the second mass strikes the ground.

Step 5: Calculating the Final Answer

Substitute $V_0=20\sqrt{2}\text{m/s}$, $\theta ={45}^{\circ }$, and $g=10{\text{m/s}}^2$ into the equations above to find the value of $n$.

Perform the calculations to determine the final value of $n$.

By following these steps, you can determine the value of $n$ based on the given scenario.