Question

A ball is projected with a speed of 20m/s at an angle 30° from a point on the top of a high tower. the time after which its velocity becomes perpendicular to the velocity of projection

Answer 1

when a body is projected with speed u inclined Ф with horizontal .
Then, velocity of projection , U = ucosФi + usinФj ,
Let after t time body will be perpendicular upon velocity of projection.so, velocity after t time , V = ucosФi + (usinФ - gt)j.
∵ velocity of projection and velocity after t time is perpendicular upon each other. ∴ U.V = 0
⇒(ucosФi + usinФj).[ucosФi + (usinФ - gt)j] = 0
⇒u²cos²Ф + u²sin²Ф - usinФgt = 0
⇒u²[cos²Ф + sin²Ф ] = ugtsinФ
⇒u² = ugtsinФ
⇒u = gtsinФ
Hence, t = u/gsinФ

So, we have a important formula to solve this question easily
e.g., t = u/gsinФ
Here given,
u = 20 m/s and Ф = 30°
∴ t = 20/10sin30° = 20/5 = 4

Hence, t = 4 sec

Answer 2

Answer:

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