A ball is dropped from the roof of a tall building and simultaneously another ball is through horizontally with some roof
which ball lands first? explain your answer
Answers
Answer:
Step-by-step explanation:
Let ℎ
h
be the height of the tall building.
For dropped ball:
Let
t_1
be the time taken by the dropped ball to reach the ground.
Initial velocity , u=0, Acceleration , a= + g
Distance travelled, s=h, Time of travel , =1
t
=
t
1
From the equation of motion, =+122
s
=
u
t
+
1
2
a
t
2
we can write
ℎ=0×1+12××21⇒ℎ=1221⇒21=2ℎ
h
=
0
×
t
1
+
1
2
×
g
×
t
1
2
⇒
h
=
1
2
g
t
1
2
⇒
t
1
2
=
2
h
g
(or) 1=2ℎ‾‾‾√
t
1
=
2
h
g
____(1)
For horizontally projected ball:
If the ball is thrown horizontally then its initial velocity along vertical direction is zero and in this case let
t_2
be the time taken by the ball to reach the ground.
Again from the equation of motion,
=+122
s
=
u
t
+
1
2
a
t
2
we write,
⇒ℎ=0×2+12×22
⇒
h
=
0
×
t
2
+
1
2
g
×
t
2
2
⇒ℎ=1222
⇒
h
=
1
2
g
t
2
2
,
⇒22=2ℎ
⇒
t
2
2
=
2
h
g
or2=2ℎ‾‾‾√
t
2
=
2
h
g
______(2)
From equation s (1) and (2) 1=2
t
1
=
t
2
i.e., both the balls reach the ground in the same time.