770
Problem Index
1.20 A packet is dropped from an ascending balloon at 9.8 m/s at a height of 98 m.
To find time for the packet to reach the ground.
1.21 Time of ascent/time of descent and initial speed/final speed when a body is
thrown up with heavy air resistance.
1.22 Motion of a body in free fall with air resistance proportional to velocity.
1.23 In prob. (1.22) air resistance is proportional to the square of velocity.
1.24 Under the assumption of velocity square air resistance to find h to which a
body will rise when projected upwards with velocity u.
1.25 Loss in kinetic energy when a body thrown upwards returns with air resistance.
1.26 Given velocity components dx/dt = 6 + 2t and dy/dt = 4 + t, to find x(t)
and y(t), v and a.
1.27 Two objects are projected horizontally in opposite directions with velocity u 1
and u 2 from a tower. To find time when v 1 is ⊥ to v 2 and the distance of
separation.
1.28 An object projected up from the foot of a tower crosses the top of a tower in
time t 1 and recrosses it in time t 2 . If t 3 is the time for free fall from the top of
tower then t 3 =
√
t 1 t 2 .
1.29 Maximum range of a shell fixed at angle θ up an incline of α is obtained when
θ = α/2 + π/4.
1.30 A stone thrown from ground over horizontal ground just clears three walls
separated by r and 2r . The inner wall is 15/7 as high as the outer ones which
are equally high. To find n if R = nr.
1.31 The velocity and angle of projection so that a ball may be thrown through two
openings in the windows of a house.
1.32 Monkey and hunter problem.
1.33 To show (a) tan α = 4h/R and (b) h = gT 2 /8.
1.34 T , R and time to reach y max and shape of flight.
1.35 Explosion of a projectile at the highest point of the trajectory.
1.36 Radius of curvature of the trajectory of a projectile.
1.37 Path of a boat which is rowed with constant velocity equal to that of the river,
with the flow always directed towards the opposite point to the starting point.
1.38 A ball thrown from a height against a wall bounces and hits the ground. To
locate the landing spot.
1.39 Three forces acting on a particle as in the diagram.
1.40 Torque, angular acceleration and angular velocity.
1.41 Minimum coefficient of friction to prevent a container from sliding in an accelerated track.
1.42 Minimum force required for a wheel to climb up an obstacle.
1.43 Centre of mass of a semicircular wire.
1.44 Centre of mass of a semicircular disc.
1.45 Centre of mass of a solid hemisphere.
1.46 Centre of mass of a hollowed circular disc.
1.47 Centre of mass of the earth–moon system.
1.48 Centre of mass of CO molecule.
1.49 Centre of mass of NH 3 molecule.
Problem Index
1.20 A packet is dropped from an ascending balloon at 9.8 m/s at a height of 98 m.
To find time for the packet to reach the ground.
1.21 Time of ascent/time of descent and initial speed/final speed when a body is
thrown up with heavy air resistance.
1.22 Motion of a body in free fall with air resistance proportional to velocity.
1.23 In prob. (1.22) air resistance is proportional to the square of velocity.
1.24 Under the assumption of velocity square air resistance to find h to which a
body will rise when projected upwards with velocity u.
1.25 Loss in kinetic energy when a body thrown upwards returns with air resistance.
1.26 Given velocity components dx/dt = 6 + 2t and dy/dt = 4 + t, to find x(t)
and y(t), v and a.
1.27 Two objects are projected horizontally in opposite directions with velocity u 1
and u 2 from a tower. To find time when v 1 is ⊥ to v 2 and the distance of
separation.
1.28 An object projected up from the foot of a tower crosses the top of a tower in
time t 1 and recrosses it in time t 2 . If t 3 is the time for free fall from the top of
tower then t 3 =
√
t 1 t 2 .
1.29 Maximum range of a shell fixed at angle θ up an incline of α is obtained when
θ = α/2 + π/4.
1.30 A stone thrown from ground over horizontal ground just clears three walls
separated by r and 2r . The inner wall is 15/7 as high as the outer ones which
are equally high. To find n if R = nr.
1.31 The velocity and angle of projection so that a ball may be thrown through two
openings in the windows of a house.
1.32 Monkey and hunter problem.
1.33 To show (a) tan α = 4h/R and (b) h = gT 2 /8.
1.34 T , R and time to reach y max and shape of flight.
1.35 Explosion of a projectile at the highest point of the trajectory.
1.36 Radius of curvature of the trajectory of a projectile.
1.37 Path of a boat which is rowed with constant velocity equal to that of the river,
with the flow always directed towards the opposite point to the starting point.
1.38 A ball thrown from a height against a wall bounces and hits the ground. To
locate the landing spot.
1.39 Three forces acting on a particle as in the diagram.
1.40 Torque, angular acceleration and angular velocity.
1.41 Minimum coefficient of friction to prevent a container from sliding in an accelerated track.
1.42 Minimum force required for a wheel to climb up an obstacle.
1.43 Centre of mass of a semicircular wire.
1.44 Centre of mass of a semicircular disc.
1.45 Centre of mass of a solid hemisphere.
1.46 Centre of mass of a hollowed circular disc.
1.47 Centre of mass of the earth–moon system.
1.48 Centre of mass of CO molecule.
1.49 Centre of mass of NH 3 molecule.