4
1 Kinematics and Statics
1.5 A man of height 1.8 m walks away from a lamp at a height of 6 m. If the man’s
speed is 7 m/s, find the speed in m/s at which the tip of the shadow moves.
1.6 The relation 3t =
√
3x + 6 describes the displacement of a particle in one
direction, where x is in metres and t in seconds. Find the displacement when
the velocity is zero.
1.7 A particle projected up passes the same height h at 2 and 10 s. Find h if g =
9.8 m/s 2 .
1.8 Cars A and B are travelling in adjacent lanes along a straight road (Fig. 1.2).
At time, t = 0 their positions and speeds are as shown in the diagram. If car A
has a constant acceleration of 0.6 m/s 2 and car B has a constant deceleration of
0.46 m/s 2 , determine when A will overtake B.
[University of Manchester 2007]
Fig. 1.2
1.9 A boy stands at A in a field at a distance 600 m from the road BC. In the field
he can walk at 1 m/s while on the road at 2 m/s. He can walk in the field along
AD and on the road along DC so as to reach the destination C (Fig. 1.3). What
should be his route so that he can reach the destination in the least time and
determine the time.
Fig. 1.3
1.10 Water drips from the nozzle of a shower onto the floor 2.45 m below. The drops
fall at regular interval of time, the first drop striking the floor at the instant the
third drop begins to fall. Locate the second drop when the first drop strikes the
floor.
1.11 The velocity–time graph for the vertical component of the velocity of an object
thrown upward from the ground which reaches the roof of a building and
returns to the ground is shown in Fig. 1.4. Calculate the height of the building.
1 Kinematics and Statics
1.5 A man of height 1.8 m walks away from a lamp at a height of 6 m. If the man’s
speed is 7 m/s, find the speed in m/s at which the tip of the shadow moves.
1.6 The relation 3t =
√
3x + 6 describes the displacement of a particle in one
direction, where x is in metres and t in seconds. Find the displacement when
the velocity is zero.
1.7 A particle projected up passes the same height h at 2 and 10 s. Find h if g =
9.8 m/s 2 .
1.8 Cars A and B are travelling in adjacent lanes along a straight road (Fig. 1.2).
At time, t = 0 their positions and speeds are as shown in the diagram. If car A
has a constant acceleration of 0.6 m/s 2 and car B has a constant deceleration of
0.46 m/s 2 , determine when A will overtake B.
[University of Manchester 2007]
Fig. 1.2
1.9 A boy stands at A in a field at a distance 600 m from the road BC. In the field
he can walk at 1 m/s while on the road at 2 m/s. He can walk in the field along
AD and on the road along DC so as to reach the destination C (Fig. 1.3). What
should be his route so that he can reach the destination in the least time and
determine the time.
Fig. 1.3
1.10 Water drips from the nozzle of a shower onto the floor 2.45 m below. The drops
fall at regular interval of time, the first drop striking the floor at the instant the
third drop begins to fall. Locate the second drop when the first drop strikes the
floor.
1.11 The velocity–time graph for the vertical component of the velocity of an object
thrown upward from the ground which reaches the roof of a building and
returns to the ground is shown in Fig. 1.4. Calculate the height of the building.