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Two small balls A and B are projected in same vertical plane simultaneously with same speed of 20m/s at t = 0. Ball A has an initial horizontal velocity and B has initial velocity at an angle  above the line joining A and B as shown. If the projectiles collide in mid air at time t, then t=?

Two small balls A and B are projected in same vertical plane simultaneously with same speed of 20m/s at t = 0. Ball A has an initial horizontal velocity and B has initial velocity at an angle  above the line joining A and B as shown. If the projectiles collide in mid air at time t, then t=?
 

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Grade:12

1 Answers

Liza Singla
13 Points
4 years ago
hLet the angle next to theta be alpha. ​
Therefore, tan alpha= 100/ 100 sqrt 3 => alpha= 30 degrees. 
Since, alpha is the alternate angle to the angle of A( velocity 20m/s) and the distance AB. Therefore, it’s also equal to 30 as well. 
 
Breaking 20m/s into components- 20Sin 30( perpendicular to ab) and 20 cos 30( along ab). Similarly, breaking the 20m/s velocity on the lower end on AB into 20 Sin theta ( perpendicular to BA) and 20 Cos theta( along BA) 
With respect to A, ball B will move in the line AB. Hence, 
20 Sin30= 20 Sin theta 
Therefore, theta= 30 degrees. 
AB= square root (100)2+ ( 100* sqrt 3)2
AB= 200m 
Using the distance times relation, t= s/v 
t= 200/ 20 Cos30 + 20 Cos 30
t= 10/ sqrt  3 seconds 
 

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