Kinematics 2
1.
The figure below shows the path of water from a hose pipe.
hose pipe
7.0 m s-1
P
path of
water
1.3 m
ground
3.6 m
The end of the horizontal hose pipe is at a height of 1.3 m from the ground. The initial horizontal
velocity of the water is 7.0 m s–1. The horizontal distance from the end of the hose pipe to the point
where the water hits the ground is 3.6 m. You may assume that air resistance has negligible effect
on the motion of the water jet.
(a)
On the figure above, draw an arrow to show the direction of the acceleration of the water at
point P.
(Mark this arrow A).
[1]
(c)
Explain why the horizontal component of the velocity remains constant at
7.0 m s–1.
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[1]
(d)
Show that the water takes about 0.5 s to travel from the end of the pipe to the ground.
[1]
(e)
Show that the speed of the water when it hits the ground is 8.6 m s–1.
[3]
[Total 6 marks]
2.
The figure below shows the path of a ball thrown from A and passing through positions B, C and
D.
The ball is thrown from A with a velocity v. A vector arrow on the figure. represents the magnitude
and direction of the velocity of the ball at A.
(a)
On the figure draw arrows to represent the horizontal and vertical components of the velocity
of the ball at A.
[1]
(b)
State how the components of the velocity of the ball at B, C and D compare with the
components at A. Assume air resistance is negligible.
(i)
The vertical component at B
............................................................
The horizontal component at B
.........................................................
[1]
(ii)
The vertical component at C
...............................................................
The horizontal component at C
.........................................................
[1]
(iii)
The vertical component at D
The horizontal component at D
............................................................
.........................................................
[1]
(c)
Explain the answers you have given for the components of the velocity of the ball at positions
B, C and D.
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[4]
[Total 8 marks]
3.
A champion BMX cyclist wishes to become a professional and seeks help from an A-level Physics
student in creating an act. The student suggests two stunts; one involving a horizontal take-off on
to a sloping ramp and the other involving a loop-the-loop manoeuvre.
(a)
The student begins by finding out the maximum speed the cyclist can produce on level
ground. Two flags are positioned 240 m apart on a flat road. The cyclist is told to accelerate
to the first flag and to pedal as hard as he can until the second flag is passed. This is shown
in Fig. 1
240 m
The student gets the cyclist to repeat the test three times and records the following results:
14.8 s
17.2 s
15.6 s
Show that the mean speed the cyclist can maintain over the 240 m is about 15 m s–1.
[2]
(b)
The student designs the stunt shown in the figure below where the cyclist must take off at 15
m s–1 from a horizontal launch pad and land smoothly just at the edge of a sloping ramp.
15 m s–1
launch pad
y
x
ramp
45°
ground
The student reasons that in order to land smoothly, the direction of the velocity of the cyclist
on reaching the edge of the ramp must be at the same 45° angle as the ramp itself.
Ignore air resistance in all calculations.
(i)
Explain why the vertical component of velocity on reaching the ramp must be 15 m s–1.
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[1]
(ii)
The student calculated the vertical fall y to the ramp to be about 11 m. Show how he
arrived at this result.
[2]
(iii)
The student calculated the horizontal jump x to the ramp to be about 23 m. Show how
he arrived at this result.
[1]
[Total 6 marks]
4
[7]
mar
ks
5
(You’ll need to look this one up in the textbook)