From the red dashed red triangle on the picture one can measure the shooting angle to be θ = (22 ± 3?). Using the scale of the graph and attached to the exam “ruler” one can measure the maximum height above the end of the shooter h =( 9 ± 2) m and the horizontal distance from the end of the shooter to the place of maximum height L = (33 ± 2) m as well as the height H = 35m from the maximum to the drop point and total range? L’ = (83 ± 2) m
From the conservation of energy we have:
mgh + m(vcosθ)2/2 =? mv2/2
v = √2gh/(1-cosθ)2 = ?√2gh/sinθ2 = 35 ± 8 m/s
Horizontal speed is vh= v cosθ = 32 m/s and it should be constant without air resistance. Due to acceleration g it should take t1 =√2h/g = 1.3??? to reach height h and? t2 = √2H/g??? = 2.7 s to drop to the bottom.? During this time gravel should cover a distance of about 140 m. The observed range is much smaller (83 m) due to the air resistance.
The average horizontal speed is about
va = 83/4 = 21 m/s.
The final speed is:
va = (vh+vf)/2? vf = 2va? - vh? = 7 m/s
so the negative acceleration due to air resistance is
vf = vh – at??? a = (vh – vf)/t = 6m/s2
So the force acting on (for example) 1 kg of gravel was about 10 N. It is clear from the photograph that it strongly depend on the size of stones.
There were many ways to solve this problem and all the fully correct ones were awarded full marks and partly correct ones part marks.? ?