Question

Question 4.15 The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m s–1 can go without hitting the ceiling of the hall?

Chapter Motion In A Plane Page 87

Answer 1

Given,
Hight of Hall( H) = 25 m
Let ball is thrown with speed 40m/s at an angle ∅ with horizontal .

We know,
H = u²sin²∅/2g
25= (40)² × sin²∅/2× 10
25 = 80 × sin²∅
Sin²∅ = 25/80
Sin∅ = 5/4√5
Cos∅ = √55/4√5

Now, horizontal range = u²sin2∅/g
= (40)²× 2sin∅×cos∅/g
= 160 × 2 × 5/4√5 × √55/4√5
= 20√55 m

Answer 2

Hi friend,

Given:- The ceiling of hall is 25 m high 

=> The max. height attained by the ball will be 25m.

=> H = 25m, u = 40 m/s  [given]

we know that,

H  =  u2sin2θ / 2g

=> sin2θ = 2gH / u2   

               = 2 x 9.8 x 25 / ( 40 )2  

               = 0.30625

=> sin  θ = 0.5534

=> θ = 33.6 o

Hence, R = u2sinθ / g  =  (40)2  sin 67.2o /9.8

                                              =  150.5 m

Hope it helps!