Physics โ Problems and solutions
1. A particle starts from the origin ๐๐ and moves in a horizontal plane with a constant
acceleration (โ2,1) cm/s, respectively, the unit of distance being 1 cm on each axis.
The initial velocity of the particle is (9, โ4). Show that the position vector of the
particle after 5 seconds is (20,โ7.5); Find the position vector of the particle after ๐ก๐ก
seconds, and hence show that the particle moves along the curve ๐ฅ๐ฅ2+ 4๐ฅ๐ฅ๐ฅ๐ฅ+ 4๐ฅ๐ฅ2โ
8๐ฅ๐ฅโ18๐ฅ๐ฅ= 0.
2. A cannon of mass ๐๐2=16 ร103 kg is fixed on a movable platform of mass ๐๐3=
3 ร 103 kg which is at rest on a rough floor. The elevated angle of the barrel is 60 ยฐ
and the mass of the bomb is ๐๐1=50 kg. If the bomb is fired with speed ๐ฃ๐ฃ1 relative to
the barrel, the platform recoils a total distance of 3 m before it comes to rest in 6
seconds. Find ๐ฃ๐ฃ1. What is the assumption you have made? And why you can make
this?
3. A wave on a string is described by the following equation
๐๐=(15 ๐๐๐๐)cos ๏ฟฝ๐๐
5 ๐๐๐๐๐ฅ๐ฅโ ๐๐
12 ๐ ๐ ๐ก๐ก๏ฟฝ
(a) What is the amplitude of this wave?
(b) What is its wavelength?
(c) What is its period?
(d) What is its speed?
(e) In which direction does the wave travel?
