The table below shows the height , measured in the nearest cm, of 101 pawpaw trees.

1. State the modal class                                    (1mk)

2. Calculate to 2 decimal places:

1. The mean height                                                 (4mks)

2. The difference between the median and the mean height.      (5mks)

A ray of light travels from air through multiple layers of transparent media 1 , 2 and 3 whose boundaries are parallel as shown in the figure below.

Calculate:

1. Angle                             (3mks)

2. The refractive index of medium 2           (3mks)

3. The speed of light in medium 1  (speed of light in air = 3.0 X 10⁸m/s)     (3mks)

4. The refractive index of medium 3 with respect to medium 1          (3mks)

A mark on a paper is viewed normally through a rectangular block of transparent material as shown

If the speed of light in the material is 1.25 X 10⁸m/s. Calculate:

1. The apparent depth .  given that the speed of light in air is 3.0 X 10⁸m/s    (3mks)

2. The vertical displacement of the mark.  (2mks)

The diagram below shows a ray of light incident on the glass-air interface, angle i is slightly larger than the critical angle of the glass.

State and explain what would be observed on the ray of light if a drop of water was placed at the point of incidence O.                       (2mks)

Given that the velocity of light in water is 2.27 X 10⁸m/s and in glass is 2.1 x 10⁸m/s , calculate the size of angle  below.    (3mks)

The figure below shows a glass prism of refractive index 1.5 with equilateral triangle cross section. Find the angle of deviation D.      (3mks)

The figure below shows how refraction occurs

Which of the two media is denser? Explain.                    (2mks)

1. During a KDF forces training a soldier shot a bullet vertically upwards at a speed of 200m/s after a second bullet shot by trainer started to fall from maximum height of 1km. calculate:

1. The time it takes for the two bullets to meet.                                  (3mks)

2. The distance from the ground where the two bullets met.             (3  mks)

2. A car initially moving with a velocity of 50m/s decelerates uniformly at 5m/s2 for 6 seconds , it then maintained a constant speed for 4 seconds before decelerating uniformly to rest in 2 seconds.

1. Sketch a velocity-time graph for the motion            (1mk)

2. Use your sketch to find:

1. The decelaration for the last part of the journey.          (1mks)

2. The total distance moved by the car.            (3mks)

3. A suspected gang vehicle escapes with a punctured fuel tank after being shot by a chase police unit along the highway. Drops of petrol from the tank fall on the road after every 5 seconds. The distance from the first drop to the second is 5m . 20 more drops fall as the vehicle accelerates before the tank empties. The two last drops fall 50m apart. Determine the:

1. Initial velocity of the car.                                           (2mks)

2. Final velocity of the vehicle just before it ran out of fuel.           (2mk)

3. The acceleration of the car.           (2mks)

A bullet of mass 40g is fired from a gun of mass 30kg and exits the muzzle at 300m/s. The bullet travels horizontally to hit a stationary wooden block 30m away after 0.5 seconds. Determine :

1. The recoil velocity of the gun                                                (3mks)

2. The force with which the bullet hits the wooden block                       (3mks)

The figure below shows a conical flask with some water to the level indicated.

1. State the change in the stability of the flask when more water is added to it.     (1mk)

2. Give a reason for your answer in (a) above.             (1mk)