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A particle is projected from point O with velocity u in a direction making an angle α with the horizontal. At any instant its position is at point p at right angles to the initial direction of projection, Its velocity at point p is:
Horizontal velocity at point O = u cos α
Horizontal velocity at point P = v sin α
In projectile motion horizontal, component of velocity remains constant throughout the motion
∴ v sin α = u cos α
⇒ v = u cot α
Pankaj and Sudhir are playing with two different balls of masses m and 2m, respectively. If Pankaj throws his ball vertically up and Sudhir at an angle θ, both of them stay in our view for the same period. The height attained by the two balls are in the ratio:
Time of flight for the ball thrown by pankaj,
Time of flight for the ball thrown by sudhir,According to problem,
Height of the ball thrown by pankaj,
Height of the thrown by sudhir,
A ship A sailing due east with a velocity of 10 km/h happens to appear sailing due north with a velocity of 5 km/h, to a person, sitting in a moving ship B. Determine the velocity (absolute) of ship B.
.
Here we are given velocity of 'A',
Velocity of 'A', w.r.t. 'B',
Now,
Hence velocity of B,
i.e. S of E
A boy projects a stone vertically perpendicular to the trolley car with a speed v. If the trolley car moves with u constant velocity m, the time of flight of the stone is:
v = v_{0 }sin θ
u = v_{0 }cos θ
Time of flight depends on vertical component of velocity.
Which of the following statements is false for a particle moving in a circle with a constant angular speed?
In circular motion we know the velocity vector is tangent to the circle. If a particle moves in a circle with constant angular speed it perform uniform circular motion. In uniform circular motion the tangential acceleration of the particle is zero. The particle moves under radial acceleration only which points to the centre of the circle. Hence the velocity and acceleration vectors are perpendicular to each other.
A particle is moving on a circular path of radius r with uniform velocity v. The change in velocity when the particle moves from P to Q is (∠POQ=40^{∘}).
Change in velocity:
A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following.
Due to constant velocity along horizontal and vertical downward force of gravity stone will hit the ground following parabolic path.
An aeroplane is flying horizontally with a velocity of 600 km/h at a height of 1960 m. When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is:
Horizontal displacement of the bomb AB = Horizontal velocity × time available
A ball is rolled off the edge of a horizontal table at a speed of 4 m/second. It hits the ground after 0.4 second. Which statement given below is true.
Vertical component of velocity of ball at point P
Horizontal component of velocity = initial velocity
So the speed with which it hits the ground,
and
⇒ θ = 45º
It means the ball hits the ground at an angle of 45^{∘} to the horizontal.
Height of the table
Horizontal distance travelled by the ball from the edge of table, h = ut = 4 × 0.4 = 1.6 m
A particle is dropped from a height and another particle is thrown in horizontal direction with speed of 5 m/sec from the same height. The correct statement is:
For both cases,
Because vertical downward component of velocity will be zero for both the particles.
A projectile fired with initial velocity u at some angle θ has a range R. If the initial velocity be doubled at the same angle of projection, then the range will be:
If initial velocity be doubled then range will become four times.
Assertion: In projectile motion, the angle between the instantaneous velocity and acceleration at the highest point is 180^{∘}.
Reason: At the highest point, velocity of projectile will be in horizontal direction only.
At the highest point, vertical component of velocity becomes zero so there will be only horizontal velocity and it is perpendicular to the acceleration due to gravity.
Assertion: The maximum horizontal range of projectile is proportional to square of velocity.
Reason: The maximum horizontal range of projectile is equal to maximum height attained by projectile.
when θ = 45º, R_{max }∝ u^{2}
^{}
when θ = 90º, H_{max }∝ u^{2}
It is clear that,
The radius vector describing the position of the particle A relative to origin.
Find the rectangular components of the average velocity in the time interval between t and t + Δ t.
The radius vector describing the position of the particle A relative to origin.
Which of the following statements are true about the motion.
For these, it is clear that all the four options are correct
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