The angle between the sheet and the horizontal bench is $$$\theta$$$. The height of the point of contact of the ball and the sheet is $$$z$$$. The horizontal distance travelled by the ball between its points of contact with the sheet and the bench is $$$d$$$, as shown in Fig. 1.1. It is suggested that $$$d$$$ is related to $$$\theta$$$ by the relationship $$\[ d=\frac{P v^{2} \sin 4 \theta}{g}+Q \sqrt{z} \]$$ where $$$v$$$ is the speed of the ball as it makes contact with the sheet, $$$g$$$ is the acceleration of free fall, and $$$P$$$ and $$$Q$$$ are constants. Plan a laboratory experiment to test the relationship between $$$d$$$ and $$$\theta$$$. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine values for $$$P$$$ and $$$Q$$$. In your plan you should include: - the procedure to be followed - the measurements to be taken - the control of variables - the analysis of the data - any safety precautions to be taken. ［15］

Physics

IGCSE&ALevel

CAIE

Exam No：9702_s25_qp_54 Year：2025 Question No：1

Answer:

Knowledge points:

1.3.1 understand that the avogadro constant Na is the number of atoms in 0.012kg of carbon-12

1.3.2 use molar quantities where one mole of any substance is the amount containing a number of particles equal to the avogadro constant Na

2.1.1 define and use distance, displacement, speed, velocity and acceleration

2.1.2 use graphical methods to represent distance, displacement, speed, velocity and acceleration

2.1.3 determine displacement from the area under a velocity-time graph

2.1.4 determine velocity using the gradient of a displacement-time graph

2.1.5 determine acceleration using the gradient of a velocity-time graph

2.1.6 derive, from the definitions of velocity and acceleration, equations that represent uniformly accelerated motion in a straight line

2.1.7 solve problems using equations that represent uniformly accelerated motion in a straight line, including the motion of bodies falling in a uniform gravitational field without air resistance

2.1.8 describe an experiment to determine the acceleration of free fall using a falling body

2.1.9 describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpendicular direction

3.1.1 understand that mass is the property of a body that resists change in motion

3.1.2 recall the relationship F=ma and solve problems using it, appreciating that acceleration and resultant force are always in the same direction

3.1.3 define and use linear momentum as the product of mass and velocity

3.1.4 define and use force as rate of change of momentum

3.1.5 state and apply each of Newton’s laws of motion

5.1.1 give examples of energy in different forms, its conversion and conservation, and apply the principle of conservation of energy to simple examples

5.2.1 derive, from the equations of motion, the formula for kinetic energy

5.2.2 recall and apply the formula

5.2.4 understand and use the relationship between force and potential energy in a uniform field to solve problems

5.2.5 derive, from the defining equation W = Fs, the formula DEp = mgDh for potential energy changes near the Earth’s surface

5.2.6 recall and use the formula DEp = mgDh for potential energy changes near the Earth’s surface

6.3.3 distinguish between gravitational potential energy and elastic potential energy

Answer:

Knowledge points:

Solution:

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