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 5

 A car travels anticlockwise along a horizontal circular road of radius 12 m, as shown. 

The car takes a time of 4.0 s to move from position P to position Q. 

What is the magnitude of the average velocity of the car for the journey from P to Q? 

A 4.2 m s^–1 

B 4.7 m s^–1 

C 6.0 m s^–1 

D 14 m s^–1

ANSWER: A

The Physics Behind

• Average velocity v of an object that has moved a displacement d in time t is 

v = d / t

• The time t is given [4.0 s]. The displacement d however needs to be calculated first and this is the straight line distance from P to Q.
• You should see that you can have a right triangle with the sides measuring 12 m each.
• The hypotenuse is the d. Using Pythagorean Theorem you should get d = 17 m.
• For the v, divide 17 m by 4.0 s.
• The answer therefore is A.

9702_s22_qp_11 Question 9

A projectile is launched at an angle above horizontal ground and travels through the air. 

Assume that no upthrust acts on the projectile. 

Which diagram shows the directions of the force or forces acting on the projectile at position X?

ANSWER: B

The Physics Behind answer

• Before reaching peak or point X,
• a velocity-dependent drag acts on the projectile, opposing the motion,
• this can be pictured as two drag components acting in the opposite directions of the vertical and horizontal velocities,
• downward gravity also acts on the projectile.
• When the projectile is at point X,
• the air resistance along the horizontal remains as the horizontal velocity is maintained along the horizontal [zero resultant force along horizontal so no change is velocity],
• the air resistance along the vertical is gone as it is velocity-dependent i.e. vertical velocity is zero at X, but the gravity is remains acting on the projectile's mass
• there are 2 forces and can be represented by vector arrows in option B.

9702_s22_qp_11 Question 6

A ball is thrown horizontally with a speed of 10.0 m s^–1 above horizontal ground. The ball hits the ground after a time of 3.0 s. 

Air resistance is negligible. 

What is the speed of the ball just before it hits the ground? 

A 10 m s^–1 

B 29 m s^–1 

C 31 m s^–1 

D 39 m s^–1  

ANSWER: C

The Physics Behind 

• The speed is the magnitude of the velocity of ball just before it hits the ground.
• This can be calculated using the Pythagorean Theorem

v² = v_x² + v_y²

where v_x is the horizontal speed and v_y is the vertical speed 

• The vertical speed v_y can be calculated using the equation of motion [from definition of acceleration],

v_y = u + at

where u is initial vertical speed [zero] and t is 3.0 s.

9702_s22_qp_11 Question 5

The curved line PQR is the velocity–time graph for a car starting from rest. 

What is the average acceleration of the car over the first 5 s? 

A the area below the curve PQ 

B the area of the triangle PQS 

C the gradient of the straight line PQ 

D the gradient of the tangent at Q 

ANSWER: C

The Physics Behind

• Options A and B give distance.
• Option D tells the instantaneous acceleration.
• Average acceleration is the gradient of the line PQ. This means that the instantaneous acceleration varies with time from 0 to 5 s, that is from a lower value changing at constant rate to a higher value. The gradient of line PQ gives the average of these acceleration values within this time interval.

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 7

A small glider moves along a horizontal air track as shown.  

At each end of the air track, the glider has a perfectly elastic collision with a fixed buffer. 

The glider moves at a constant speed between collisions. 

Which graph represents the variation with time t of the velocity v of the glider as it moves between the two buffers?  

ANSWER: D

The Physics behind the answer:

• By "has a perfectly elastic collision" it means that the kinetic energy of the glider is conserved.
• This means further that, for each collision, the speed of the glider remains the same.
• It is only the direction of the glider that changes at every collision.
• Since the options A, B, C and D are all velocity-time graph i.e. speed plus the directions, following the Cartesian plane conventions it is D that tells that speed [or magnitude of velocity] doesn't change while directions do every collision with the fixed buffers.

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.