9702_s22_qp_22 Question 3

 

9702_s22_qp_12 Question 9

 A stone S and a foam rubber ball R are identical spheres of equal volume. They are released from rest at time t = 0 and fall vertically through the air. Both reach terminal velocity. 

Which graph best shows the variation with time t of the speed v of the stone and of the rubber ball?

ANSWER: B

The Physics Behind

• The terminal velocity is reached by an object that are released from rest is reached when the resultant force has already become zero which means that
• the acceleration is also zero [Newton's 2nd Law of Motion] and
• the velocity remains the same [from definition of acceleration, that is, no more change in velocity].
• The resultant force is the sum of the forces acting on objects.
• One force is the downward gravity [weight]
• The other is air resistance dependent on both the surface area and speed of object
• As the object moves down, it speeds up and therefore the air resistance is getting stronger and stronger. The resultant force then is becoming smaller and smaller. However, there is a difference between the objects S and R as though the air resistance on them is same at same speed, stone R is heavier than rubber R. 
• The above means that R can have resultant force of 0 [or zero acceleration or terminal velocity] faster than S.
• Option B is the answer.

9702_s22_qp_12 Question 6

 The water surface in a deep well is 78.0 m below the top of the well. A person at the top of the well drops a heavy stone down the well. 

Air resistance is negligible. The speed of sound in the air is 330 m s^–1. 

What is the time interval between the person dropping the stone and hearing it hitting the water? 

A 3.75 s 

B 3.99 s 

C 4.19 s 

D 4.22 s

ANSWER: D

The Physics Behind

• The time interval x between the person dropping the stone and hearing it hitting the water can be determined by calculating
• the time t₁ when the stone hits the water and produce sound
• the time t₂ when sound travels upwards and  reach the person's ear
• adding t₁ and t₂.
• For time t₁, the motion is freefall/at uniform acceleration so use the equation of motion s = ut₁  + 1/2 at₁²

78.0 = 0 + 1/2 (9.8) t₁² 

t₁² =15.92

t₁ =  3.99 s

• For time t₂, sound is a wave unaffected by gravity so use the constant speed formula v = d/t₂

t₂ = 78.0 / 330

t₂ = 0.236 s

• Therefore, answer is D.

9702_s22_qp_12 Question 4

An object is moving with an initial velocity of 4.0 m s^–1 to the right. The velocity of the object changes so that its final velocity is 3.0 m s^–1 downwards, as shown. 

Which arrow represents the change in velocity of the object? 

ANSWER: B

The Physics Behind

• The key idea here is vector addition.
• When adding quantities with direction e.g. velocities, a tip-to-tail method can be used.
• Represent each vector by an arrow with its magnitude proportional to length of arrow and direction represented by direction of arrow itself.
• With same scale, start drawing one starting from the tip of the previous [tip-to-tail].
• When done drawing all arrows, tip-to-tail, connect the tail of the first arrow drawn and tip of the last arrow using a straight arrow.
• its length is proportional to magnitude of the resultant or vector sum
• its direction is given by the arrow
• A change in a quantity e.g. change in velocity Δv, means final velocity v minus initial velocity u.
• You can rewrite  Δv = v - u as Δv = v + (- u).
• Then use the tip-to-tail, that is, draw an arrow representing one vector and draw the next vector from its tip [consider the negative as you are adding a negative as suggested by the above formula].
• Your diagram should look like final velocity drawn downward with initial velocity drawn leftward i.e. + (-v).

9702_s22_qp_13 Question 6

Two projectiles, X and Y, are fired into the air from the same place on level ground and reach the same maximum height, as shown. 

Projectile X is fired vertically upwards and projectile Y is fired at an angle to the horizontal. 

Air resistance is negligible. 

Which statement is correct? 

A X and Y are at rest at their maximum heights. 

B X and Y are fired with the same speed. 

C X and Y take the same time to return to the ground. 

D X and Y travel the same distance.  

ANSWER: C

The Physics behind the answer:

• A projectile motion can be split into 2 motions - one along the vertical and the other along the horizontal. Assuming that air resistance is negligible, the projectile
• experiences a force [gravity] along the vertical and so it will accelerate at rate 9.81 m s^-2.
• experiences no force along the horizontal i.e. zero acceleration and travels at constant horizontal velocity.
• You can say therefore that the motion of Y is the same as the motion of X along the vertical plus a constant velocity motion along the horizontal.
• This means that when sent up at the same time with the velocity of X the same as the vertical component of velocity of Y [which should be as seen in the graph], they will return to the ground at the same time as they have the same acceleration [9.81 m s^-2]. 
• The only difference is that Y has moved horizontally due to its horizontal velocity/motion.

9702_s22_qp_13 Question 10

A person stands on the edge of a high cliff that is next to the sea. The person throws a stone vertically upwards. Air resistance acts on the stone. 

The stone eventually hits the sea. 

Which velocity–time graph best shows the motion of the stone from when it is released until it hits the sea? 

ANSWER: B

The Physics behind the answer:

• A very important note here is that air resistance acts on the stone. 
• Since air resistance is acting, then the stone is experiencing a decreasing resultant force.
• A decreasing resultant force means that the stone's acceleration is also decreasing.
• In a velocity-time graph, the acceleration is the gradient of the graph.
• Among the 4 options, B shows a deceasing gradient.

Other concepts that are worth looking at:

1. The options don't use the Cartesian plane as a convention for directions. It looks like, in this case, the negative y-axis represents upwards direction.
2. If the air resistance is negligible, then the acceleration of the stone is constant and the answer would have been A.
3. If the graph is a speed-time graph [magnitude only i.e. positive values] instead of a velocity-time graph, then the answer would have been D. You may want to compare the second portion of the graph when the y-axis value is zero between option D and B.