P.3.4.1.1 Scalars and vectors

Two spheres, P and Q, have the same volume but P has a greater mass. The spheres fall in air at their terminal velocities v_P and v_Q respectively. Which row states the relationship between v_P and v_Q and the reason?

• Relationship between v_P and v_Q : v_P = v_Q

  Reason: Terminal velocity is unaffected by mass

• Relationship between v_P and v_Q : v_Q > v_P

  Reason: The mass of Q is less and it accelerates more

• Relationship between v_P and v_Q : v_Q > v_P

  Reason: P reaches equilibrium at a lower terminal velocity

• Relationship between v_P and v_Q : v_P > v_Q

  Reason: Q reaches equilibrium at a lower terminal velocity

An aircraft is flying due north through still air with a speed v

The aircraft enters a region where the wind is blowing with a speed u from a direction which makes an angle of θ with due south.

What is the time taken for the aircraft to fly a distance D due north of its current position in this windy region?

• 
• 
• 
• 

Three coplanar forces F₁, F₂ and F₃ act on a point object.

Which combination of forces can never produce a resultant force of zero?

• A

• B

• C

• D

The diagram shows a gas particle about to collide elastically with a wall.

Which diagram shows the correct change in momentum Δmv that occurs during the collision?

• 
• 
• 
• 

Which row correctly states whether momentum, mass and velocity are scalar or vector quantities?

• A

• B

• C

• D

The diagram shows the path of a projectile launched from ground level with a speed of 25 m s^–1 at an angle of 42° to the horizontal. What is the horizontal distance from the starting point of the projectile when it hits the ground?

• 23 m

• 32 m

• 47 m

• 63 m

Which of the following is a scalar quantity?

• kinetic energy

• momentum

• force

• acceleration

What is correct for the quantities impulse and force?

• A

• B

• C

• D

Which of the following is a scalar quantity?

• acceleration

• distance

• displacement

• momentum

Two forces of 6 N and 10 N act at a point. Which of the following could not be the magnitude of the result?

• 16 N

• 8 N

• 5 N

• 3 N