Past JEE question
A small block slides without friction down an inclinded plane starting from the rest. If Sn is the distance travelled form time t = n to t = n+1, then Sn/Sn+1 is
(JEE 2004, Screening)
A particle moving eastwards with a velocity 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is
b. 1/SQRT(2) m/s² towards north-west
c. ½ m/s² toward north-west
d. ½ m/s² towards north
The average acceleration must have an westward component and northward component to make the velocity towards east as zero and to make velocity towards north as 5 m/s
Hence it will act in the direction of northwest.
Westward component of average acceleration = (0-5)/10 = -½ m/s²
Northward component of average of acceleration = (5-0)/10 = ½ m/s²
Hence magnitude of average acceleration = Sqrt( (-1/2) ²+(1/2) ²) = 1/SQRT(2)
A river is flowing from west to east at a speed of 5 metres per minute. A man on the south bank of the river, capable of swimming at 10 metres per minute in still water, wants to swim across the river in the shortest time. He should swim in the direction.
a. due north
b. 30° east of north
c 30° west of north
d. 60° east of north
Answer: ( c )
Since the man wants to reach the spot opposite to him, he has to swim to towards west of north to make use of water velocity in the direction west to east.
As he travels 10 metres/ per minute in that direction, he will have a moment of 5 metres/min in the west to east direction.
So angle is given by sin θ = 5/10 = ½
θ = 30°
4. State whether the statement is true or false
Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion with the same speed. (neglect air resistance)
Both the balls thrown vertically with the same speed will reach equal height irrespective of their masses. These would also pass through the point of projection in their downward motion with the same speed when subject to acceleration due to gravity.
State whether the statement is true or false
A projectile fired form the ground follows a parabolic path. The speed of the projectile is minimum at the top of its path.
At the top of the path, the vertical component of velocity is zero and the particle has only horizontal component. Hence the speed (the magnitude of the velocity) is minimum at the top of the path.
A particle starts from rest. Its acceleration at the start is 10 m/s² and in 12 seconds the acceleration uniformly reduces to zero. The maximum speed of the particle will be
a. 20 m/s
b. 60 m/s
c. 550 m/s
d. 660 m/s
Revision question 1
A ball is dropped vertically from a height of d above the ground. It hits the ground and bounces up vertically to a height d/2. Neglecting the subsequent motion and air resistance, (a) what will be the shape of velocity versus distance diagram? (b)What will be the shape of velocity versus time diagram.
Options for A
Linear or curvilinear
Options for B
Linear or curvilinear
(Based on Past JEE questions JEE 2000, screening)
Revision Problem 2
An aeroplane has to go from a point A to another point B, 500 km away 30° east of north. A wind is blowing due north at a speed of 20 m/s. the air-speed of the plane is 150 m/s.
(a) Find the direction in which the pilot should head the plane to reach the point B.
(b) Find the time taken by the plane to go from A to B.
(Source: HC Verma, Prob. 49)