A boy is standing on the top of the building having 100 m height, he throws a ball in upward direction if ball goes 25 m high and falls back on the ground then find the distance covered and displacement done by the ball for this motion?
Answers
Answer:
he height of the building is =100 m
The first ball is thrown at the instant t=0 and another ball is thrown after a time interval of x.
Let, the initial velocity of first ball=u m/s.
The distance covered by the ball is given by:
S
1
=u(t+x)−
2
1
g(t+x)
2
On the other hand, the second ball is thrown at half the speed as of the first ball. So, the distance covered by the second ball is given by:
S
2
=
2
u
t−
2
1
gt
2
The distance between the two balls at t=2 s is 15 m.
∴S
1
−S
2
=15
Now, S
1
−S
2
=u(t+x−
2
t
)−
2
1
g(t
2
+2xt+x
2
−t
2
)
Substitute the values in above equation:
Consider the time interval x=1 since it is less than 2 sec.
15=u(1+
2
2
)−
2
1
×10(2×1×2+1)
u=
2
40
m/s=20 m/s
Therefore, velocity of first ball=20m/s in upward direction
Velocity of second ball is
2
20
=10m/s in upward direction.
Explanation:
Given Height Of building = 100m
On the top of the buildings , A boy throws the ball which goes 25 m high and fall back on the ground.
As, we Knows that distance is a scalar quantity and displacement is a vector quantity. As scalar quantity have only magnitude of object. Whereas in vector quantity have magnitude of object as well as it's direction.
- The total distance covered by ball = Ball goes in upward direction from the top of the building + Ball comes back in downward direction of its maximum level when its velocity becomes zero. + The height of the building does the ball covered when it reaches to ground .
- The total distance of ball = 25m + 25m + 100m = 150m.
As, we got the distance = 150m.
- The displacement done by ball = As displacement is only follows direction, So, ball from the top of building – comes back in the downward direction where its projected ( on the top of the building ) + The height of the building where the ball goes down to reach the ground.
- The displacement of the ball = 25m – 25m + 100m = 100m .
Also its displacement = 100m
Refer the Above Attachment for reference of the illustration image of the question.
