Advertisements
Advertisements
Question
A ball thrown up vertically returns to the thrower after 6 s. Find
- the velocity with which it was thrown up,
- the maximum height it reaches, and
- its position after 4 s.
Advertisements
Solution
a. Final velocity (v) = 0
Time (t) = 6s
g = 10m/s2
The first equation of motion
v = u + gt
0 = u + (−9.8) × 3 (negative sign due to opposite direction)
u = 30m/s
Hence, the ball is thrown upwards with a velocity of 30m/s.
b. Initial velocity (u) = 30m/s
Final velocity (v) = 0
Time (t) = 3s
the second equation of motion
h = ut + `1/2` gt2
h = `30 × 3 + 1/2 xx (−10) x (3)^2`
h = 90 − 45
h = 45m
Hence, the maximum height attained by the ball is 45m.
c. Position of the ball after 4 s Distance travelled downwards in 1 sec the second equation of motion
h = ut + `1/2` gt2
h = `0 xx 1 + 1/2 xx 10 xx (1)^2`
h = 5m
Distance covered in 1 second = 5m
Distance covered in 4 seconds = 45 − 5
= 40 m
Hence, after 4 seconds, the ball will be 40m above the ground.
APPEARS IN
RELATED QUESTIONS
A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where the two stones will meet.
Which force is responsible for the moon revolving round the earth ?
State whether the following statement is true or false :
A falling stone also attracts the earth.
A stone is thrown vertically upwards with initial velocity u reaches a height ‘h’ before coming down. Show that the time taken to go up is the same as the time taken to come down.
The total energy of an object falling freely towards the ground ______.
A body falls freely under gravity from rest and reaches the ground in time t. Write the expression for the height fallen by the body.
Write scientific reason.
The value of gravitational acceleration (g) decreases as we go deep inside the earth.
Define acceleration due to gravity.
Write a short note.
Free Fall
Read the given passage carefully and answer the questions.
We know that the force of gravity due to the earth acts on each and every object. When we were holding the stone in our hand, the stone was experiencing this force, but it was balanced by a force that we were applying on it in the opposite direction. As a result, the stone remained at rest. Once we release the stone from our hands, the only force that acts on it is the gravitational force of the earth and the stone falls down under its influence. Whenever an object moves under the influence of the force of gravity alone, it is said to be falling freely. Thus the released stone is in a free fall. In free fall, the initial velocity of the object is zero and goes on increasing due to the acceleration due to the gravity of the earth. During free fall, the frictional force due to air opposes the motion of the object and a buoyant force also acts on the object. Thus, true free fall is possible only in a vacuum.
1) Complete the following statement by choosing the right option.
The stone held in the hand is stable because on it __.
- two unbalanced forces are exerted.
- only the gravitational force of the earth is exerted.
- gravitational force of the earth is not exerted.
- two balanced forces are exerted.
2) Why does free fall not happen on the earth?
3) Why does the velocity of the object increase during the free fall?
4) Which type of force exerts on the object during free fall?
5) Why does free fall happen only in a vacuum?
