8
1 Kinematics and Statics
(iv) Show that the shape of its flight is in the form of a parabola y = bx +cx 2 ,
where b and c are constants [acceleration due to gravity g = 9.8 m/s 2 ].
[University of Aberystwyth, Wales 2004]
1.35 A projectile of mass 20.0 kg is fired at an angle of 55.0 ◦ to the horizontal
with an initial velocity of 350 m/s. At the highest point of the trajectory the
projectile explodes into two equal fragments, one of which falls vertically
downwards with no initial velocity immediately after the explosion. Neglect
the effect of air resistance:
(i) How long after firing does the explosion occur?
(ii) Relative to the firing point, where do the two fragments hit the ground?
(iii) How much energy is released in the explosion?
[University of Manchester 2008]
1.36 An object is projected horizontally with velocity 10 m/s. Find the radius of
curvature of its trajectory in 3 s after the motion has begun.
1.37 A and B are points on opposite banks of a river of breadth a and AB is at right
angles to the flow of the river (Fig. 1.4). A boat leaves B and is rowed with
constant velocity with the bow always directed toward A. If the velocity of the
river is equal to this velocity, find the path of the boat (Fig. 1.5).
Fig. 1.5
1.38 A ball is thrown from a height h above the ground. The ball leaves the point
located at distance d from the wall, at 45 ◦ to the horizontal with velocity u.
How far from the wall does the ball hit the ground (Fig. 1.6)?
Fig. 1.6
1 Kinematics and Statics
(iv) Show that the shape of its flight is in the form of a parabola y = bx +cx 2 ,
where b and c are constants [acceleration due to gravity g = 9.8 m/s 2 ].
[University of Aberystwyth, Wales 2004]
1.35 A projectile of mass 20.0 kg is fired at an angle of 55.0 ◦ to the horizontal
with an initial velocity of 350 m/s. At the highest point of the trajectory the
projectile explodes into two equal fragments, one of which falls vertically
downwards with no initial velocity immediately after the explosion. Neglect
the effect of air resistance:
(i) How long after firing does the explosion occur?
(ii) Relative to the firing point, where do the two fragments hit the ground?
(iii) How much energy is released in the explosion?
[University of Manchester 2008]
1.36 An object is projected horizontally with velocity 10 m/s. Find the radius of
curvature of its trajectory in 3 s after the motion has begun.
1.37 A and B are points on opposite banks of a river of breadth a and AB is at right
angles to the flow of the river (Fig. 1.4). A boat leaves B and is rowed with
constant velocity with the bow always directed toward A. If the velocity of the
river is equal to this velocity, find the path of the boat (Fig. 1.5).
Fig. 1.5
1.38 A ball is thrown from a height h above the ground. The ball leaves the point
located at distance d from the wall, at 45 ◦ to the horizontal with velocity u.
How far from the wall does the ball hit the ground (Fig. 1.6)?
Fig. 1.6