Question

A boy standing on a 50 m high building throws a ball vertically upwards with a velocity of 15 m per second how long will the ball take to pass by him after it is thrown how long does it take to hit the ground

Answer 1

Answer:

         

           Time taken to cross the boy = 3.46 s

              Time taken to hit the ground = 5.46 s

Explanation:

GIVEN :

height of ball thrown = 15 m

height of building = 50m

TO FIND :

        a) Time taken by ball to pass the boy

       b)  Time taken to hit the ground

Step by Step explanation :

From the equation of motion,

       s = ut +1/2gt₁²

    15m = 0 + 1/2 (10 x t²)

       t₁ = $\sqrt{3}$ = 1.73 s

same time will be taken by ball to reach back from the top most position to cross the boy (t₂) , so  t₁ = t₂

Time taken to cross the boy = t₁+t₂ = 1.732 + 1.73

         T(boy) = 3.46 s

Now , we need to ignore the height of the boy so,

    u (initial velocity ) in this case = 15m/s

     s = 50 m

     g = 10m/s²

      t = T°

∴  s = ut + 1/2gt²

   50 = 15t + 5t²

  5t² + 15t - 50 = 0

Taking 5 as a common,

t² + 3t - 10 = 0

t² + (5t - 2t ) -10 = 0

t (t+5) -2 (t+5) = 0

(t+5) (t-2) = 0

Here are two solution t = 2s or t = -5s,

Time can never be negative so, t = 2s

T° = T (boy ) + t

    = 3.46 s + 2s

T° = 5.46s

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