Question

From a certain height two bodies are simultaneously projected horizontally in opposite directions with velocities of 1 m/s and 4 m/s respectively. The time taken for the velocity vectors of the two bodies to become perpendicular to each other is ___sec.

Answer 1

Answer:

4ms and certain two bodies simounstaoesly ×1m/s with

time taken of 2m/s become perpendicular baody some of the projected body is diveds to each others so direction path

of movement force it's equal to quarrntitiy of parrllel line

titamd =4m/s -2m/s =-2m/s ×1m/s

=-1m/s

-1m/s+4m/s = 1m/s-4m/s = -3mls is answer

there fore perpendicular to each other is 3 seconds

Answer 2

Answer: 0.2 seconds

Explanation:

Concept:

When two vectors are perpendicular their dot product is equal to zero.

Calculation:

$V=u+(-gt)=u-gt$

For both the bodies:

The final velocity vectors will be:

$V_{1}=1 \hat{i}-gt\hat{j}\\V_{2}=-4 \hat{i}-gt \hat{j}$

When V₁ becomes perpendicular to V₂, at that instant the dot product of both will be zero .

Therefore,

$Since\ V_{1\perp V_{2}}: \\V_{1}.V_{2}=0\\\\\Rightarrow (\hat{i}-gt\hat{j)}\ . (-4\hat{i}-gt\hat{j})=0\\\Rightarrow -4+g^{2}t^{2}=0\\\Rightarrow g^{2}t^{2}=4\\\Rightarrow gt=2\ (g=10m/s^{2})\\\Rightarrow t=2/10=1/5=0.2s$

The velocity vectors will be perpendicular at 0.2 seconds.

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