(2) An object has an initial speed u and an acceleration a. After time t, its speed is v and it has moved through a distance s.

Transcription

1 1. Linear motion Define the term acceleration. An object has an initial speed u and an acceleration a. After time t, its speed is v and it has moved through a distance s. The motion of the object may be summarized by the equations v = u + at, s = 1 v u t. (i) State the assumption made in these equations about the acceleration a. 2 (1) (ii) Derive, using these equations, an expression for v in terms of u, s and a. 1

2 (c) The shutter speed of a camera is the time that the film is exposed to light. In order to determine the shutter speed of a camera, a metal ball is held at rest at the zero mark of a vertical scale, as shown below. The ball is released. The shutter of a camera is opened as the ball falls. 0 cm scale 196 cm camera 208 cm The photograph of the ball shows that the shutter opened as the ball reached the 196 cm mark on the scale and closed as it reached the 208 cm mark. Air resistance is negligible and the acceleration of free fall is 9.81 m s 2. (i) Calculate the time for the ball to fall from rest to the 196 cm mark. (ii) Determine the time for which the shutter was open. That is, the time for the ball to fall from the 196 cm mark to the 208 cm mark. (Total 9 marks) 2

3 2. This question is about throwing a stone from a cliff. Antonia stands at the edge of a vertical cliff and throws a stone vertically upwards. v = 8.0ms 1 The stone leaves Antonia s hand with a speed v = 8.0ms 1. The acceleration of free fall g is 10 m s 2 and all distance measurements are taken from the point where the stone leaves Antonia s hand. Sea Ignoring air resistance calculate (i) the maximum height reached by the stone (ii) the time taken by the stone to reach its maximum height..... (1) 3

4 The time between the stone leaving Antonia s hand and hitting the sea is 3.0 s. Determine the height of the cliff (3) (Total 6 marks) 4

5 3. This question is about trajectory motion. Antonia stands at the edge of a vertical cliff and throws a stone upwards at an angle of 60 to the horizontal. v = 8.0ms 1 60 Sea The stone leaves Antonia s hand with a speed v = 8.0 m s 1. The time between the stone leaving Antonia s hand and hitting the sea is 3.0 s. The acceleration of free fall g is 10 m s 2 and all distance measurements are taken from the point where the stone leaves Antonia s hand. Ignoring air resistance calculate the maximum height reached by the stone (3) the horizontal distance travelled by the stone (Total 5 marks) 5

6 4. This question is about projectile motion. A stone is thrown horizontally from the top of a vertical cliff of height 33 m as shown below. 18 m s 1 33 m sea level The initial horizontal velocity of the stone is 18 m s 1 and air resistance may be assumed to be negligible. State values for the horizontal and for the vertical acceleration of the stone. Horizontal acceleration:... Vertical acceleration:... Determine the time taken for the stone to reach sea level. (c) Calculate the distance of the stone from the base of the cliff when it reaches sea level. (1) (Total 5 marks) 6

7 5. This question is about the trajectory of a golf ball. A golfer hits a golf ball at point A on a golf course. The ball lands at point D as shown on the diagram. Points A and D are on the same horizontal level. 30m s 1 A 20m s 1 D The initial horizontal component of the velocity of the ball is 20 m s 1 and the initial vertical component is 30 m s 1. The time of flight of the golf ball between point A and point D is 6.0 s. Air resistance is negligible and the acceleration of free fall g = 10 m s 2. Calculate the maximum height reached by the golf ball. (3) the range of the golf ball. (Total 5 marks) 7

8 6. This question is about projectile motion. The barrel of a rifle is held at an angle to the horizontal. A bullet fired from the rifle leaves the barrel at time t = 0 with a speed 200 m s 1. The graph below shows the variation with time t of the vertical height h of the bullet h / m t / s Using the axes below, draw a sketch graph to show the variation of h with the horizontal distance x travelled by the bullet. (Note: this is a sketch graph; you do not have to add any values to the axes.) h x State the expression for the initial vertical component of speed V v in terms of the initial speed of the bullet and the angle. (1) 8

9 (c) Use data from the graph to deduce that the angle = 30. (The acceleration for free fall g = 10 m s 2 ) (3) (Total 6 marks) 9