31. From the top of a tower of height 40 m, a ball is projected
upwards with a speed of 20 ms at an angle of 30° to the
horizontal. If g = 10 ms?, after how long will the ball hit
the ground?
(1) 15
(2) 25
(3) 35
4) 4s
Answers
Solution :-
please refer the attachment for better understanding ,
As per the given data ,
- Height of the tower(y) = 40 m
- Angle of projection(Ф) = 30°
- Acceleration due to gravity(g) = 10 m/s²
The ball moves in a projectile from point A to B hence , the time of flight is given by ,
➝ T = 2usinФ / g
➝ T = 2 x 20 x sin 30 / 10
➝ T = 2 x 20 x 1 / 20
➝ T = 2 s
Now while moving from point B to C
By applying second equation of motion ,
➝ y = uy + at² / 2
➝ y = - u cos (60 )t + 10 x t ² / 2
➝ 40 = - 20 x 1 / 2 x t+ 5 t²
➝ 40 = - 10t + 5 t²
➝ 5t ² - 10 t - 40 = 0
➝ t ² - 2t - 8 = 0
➝ t² - 4t + 2t - 8 = 0
➝ t ( t- 4 ) + 2 ( t- 4) = 0
➝ (t + 2)( t - 4 ) =0
➝ t = -2 s or t = 4 s
We know that time cannot be negative
Hence ,
➝ t = 4 s
Hence the total time required by the ball to hit the ground
=T + t
= 2 + 4
= 6 s
The total time required by the ball to hit the ground is 6s
