To Study the Variation in Range of a Projectile with Angle of Projection

Aim  
To study the variation in range of a projectile with angle of projection.

Apparatus  
A plyboard protractor with radius of about 30 cm and marked 0 ° to 90 ° with an interval of 15 ° each, a 10-metre long measuring tape, A constant level reservoir under pressure (a tap connected to a tank or water supply line), a water pipe with a metallic nozzle (narrow opening).

Theory
The horizontal distances between point of projection and point of return, covered by the projectile during its flight, is called its horizontal range. It is represented by the symbol R.
If the water jet leaves the nozzle with a velocity U at an angle 0 with horizontal, then the
to-study-the-variation-in-range-of-a-projectile-with-angle-of-projection-1

Diagram  
to-study-the-variation-in-range-of-a-projectile-with-angle-of-projection-2

Procedure  

  1. Arrange a constant level water reservoir at one end of a horizontal slab of the laboratory.
  2. Connect a water pipe with the outlet of the reservoir and insert a metallic nozzle in the other end of the pipe held in hand.
  3. Open the water tap and check that there is no leakage of water (remove if it is there).
  4. Fix the protractor in a slot in a horizontal base to make its plane vertical and graduated surface towards yourself.
  5. Place the nozzle at the centre O of the protractor and make the jet pass through 15 ° marking on it.
  6. The jet moves along a parabola and falls back on the slab at some distance.
  7. Set the water tap such that the distance is few metres.
  8. Ask your laboratory bearer to make a mark B1 on the slab where the jet falls.
  9. Change the angle to 30 °, 45 °, 60 ° and 75 ° and repeat step 8 to get marks B2, B3, B4 and B5.
    (Do not change setting of water tap, otherwise it will change velocity U of the jet).
  10. Measure distances OB1,  OB2, OB3, OB4 and OB5 by the measuring tape. These distances give range R for different angles (and same velocity).
  11. Record your observations in the table as given below.

Observations
Least count of measuring tape = 2 cm.
Table for angle and range
to-study-the-variation-in-range-of-a-projectile-with-angle-of-projection-3

Graph  
Plot a graph between angle 0 and range R taking 0 along X-axis and R along Y-axis. The graph comes as shown below.
to-study-the-variation-in-range-of-a-projectile-with-angle-of-projection-4

Result  
From graph, we find the following two results :

  1. Range is same for two complementary angles (i.e., 15 ° and 75 ° or 30 ° and 60 °).
  2. Range is maximum for angle of projection of 45 °. ‘

Precautions  

  1. Water level in reservoir should remain constant to keep velocity of projection constant.
  2. Jet should be thin to get a sharp point of return.

Sources of error  

  1. Velocity of water jet may change during experiment.
  2. Point of return may not be sharp.

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