A ball is dropped from the top of a tower of the height of . Simultaneously, another ball was thrown upward from the bottom of the tower with a speed of ( ). These two balls would cross each other after a time:
Step 1: Given Data
Height of the tower
Acceleration due to gravity
Let the ball dropped from the top of the tower be and the ball thrown upwards from the bottom of the tower be .
The initial velocity of ball ,
The initial velocity of ball ,
Let the height from the top of the tower to the point of intersection be .
Let the height from the bottom of the tower to the point of intersection be .
Let the time taken for the intersection of the two balls be .
Step 2: Calculate the height
According to Newton's second equation of motion we get,
Step 3: Calculate the height
Since the motion of ball is against the gravity according to Newton's second equation of motion we get,
Step 4: Calculate the time
Upon adding equation and we get
Hence, the correct answer is option (D).