Question

Two partical moving in x directions such that u=3i and v=4i.due to gravition force they are coming downward direction.find their distance when both the velocities are perpendicular to each other.

Answer 1

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Answer on Question #43947 – Physics – Mechanics | Kinematics | Dynamics

Two practical moving in x directions such that u=3i and v=4i due to gravitation force they are coming downward direction. Find their distance when both the velocities are perpendicular to each other.

Solution:

Velocity of the second body considering gravitational force (g – acceleration due to gravity):

$$\vec{u} = 3\vec{i} + g t\vec{j}$$

Velocity of the second body considering gravitational force

$$\vec{v} = 4\vec{i} + g t\vec{j}$$

Two vectors are perpendicular, when their scalar product is zero:

$$\vec{u} \cdot \vec{v} = 3\vec{i} \cdot 4\vec{i} + g t\vec{j} \cdot g t\vec{j} = 12 + g^2 t^2 > 0 \Rightarrow$$

Velocities will not be perpendicular to each other.

**Answer:** both the velocities will not be perpendicular to each other.