An archer fires an arrow towards a target as shown below.
The diagram is not drawn to scale.
The centre of the target is at the same height as the initial position of the arrow. The target is a distance of 90 m from the arrow. The arrow has an initial velocity of 68 ms–1 and is fired at an angle of 11° to the horizontal.
Air resistance has negligible effect on the motion of the arrow.
Describe how the kinetic energy of the arrow changes during its journey from when it is fired until it reaches its maximum height.
Show that the time taken for the arrow to reach its maximum height is about 1.3 s.
The arrow misses the target.
Calculate the horizontal distance, measured along the base line, by which the arrow misses the target.
horizontal distance = ......................................... m
The arrow is now fired horizontally at 68 m s–1 into the target at very close range.
The arrow sticks into the target. The collision between the arrow and the target is inelastic.
i) Explain what is meant by an inelastic collision.
[1]
ii) The target is mounted on wheels. The target has a much larger mass than the mass of the arrow.
Using ideas of momentum, explain the velocity of the target immediately after the arrow sticks into the target.
[2]
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mv 2 = Fx where m is the mass of the marble and F is the constant frictional force acting on the marble.