a ball is dropped from a building of height 45 m. simultaneously another ball is thrown up with a speed of 40 m/s. calculate the relative speed of balls at any time (the).
Answers
Answer:
The relative speed of the balls as a function of time is 40 m/s.
Explanation:
Given : A ball is dropped from a building of height 45 m. Simultaneously another ball is thrown up with a speed 40 m/s.
To find : Calculate the relative speed of the balls as a function of time ?
Solution :
According to question,
When ball is dropped from the building,
The initial velocity is u_1=0\ m/su
1
=0 m/s
The velocity of the ball after time t,
v_1=u_1-gtv
1
=u
1
−gt
v_1=-gtv
1
=−gt ...(1)
When another ball which is thrown upward,
The initial velocity is u_2=40\ m/su
2
=40 m/s
The velocity of the ball after time t,
v_2=u_2-gtv
2
=u
2
−gt
v_2=40-gtv
2
=40−gt ...(2)
Relative velocity of one ball w.r.t another ball is
v_{12}=v_1-v_2v
12
=v
1
−v
2
Substitute from (1) and (2),
v_{12}=-gt+40+gtv
12
=−gt+40+gt
v_{12}=40\ m/sv
12
=40 m/s
Therefore, The relative speed of the balls as a function of time is 40 m/s.