Moderate -0.5 This is a straightforward impulse-momentum question requiring vector addition of initial and final momentum vectors at right angles, then finding the magnitude. The perpendicular condition simplifies the calculation to Pythagoras' theorem. Standard mechanics technique with clear numerical values and only 3 marks, making it easier than average even for Further Maths.
A ball has mass 0.4 kg and is hit by a wooden bat.
The speed of the ball just before it is hit by the bat is \(6 \text{ m s}^{-1}\)
The velocity of the ball immediately after being hit by the bat is perpendicular to its initial velocity.
The speed of the ball just after it is hit by the bat is \(8 \text{ m s}^{-1}\)
Show that the impulse on the ball has magnitude 4 N s
[3 marks]
Question 3:
3 | Uses vectors or diagram to show
the change in momentum | 3.3 | M1 | u = 6 i
v = 8 j
I = 0 . 4 8 j − 0 . 4 6 i
= − 2 . 4 i + 3 . 2 j
I = 2 . 4 2 + 3 2 . 2 = 4 N s
Applies the principle that impulse is
change in momentum working in
two dimensions. | 1.1a | M1
Obtains the correct magnitude,
from a valid argument | 2.1 | R1
Total | 3
Q | Marking Instructions | AO | Marks | Typical Solution
A ball has mass 0.4 kg and is hit by a wooden bat.
The speed of the ball just before it is hit by the bat is $6 \text{ m s}^{-1}$
The velocity of the ball immediately after being hit by the bat is perpendicular to its initial velocity.
The speed of the ball just after it is hit by the bat is $8 \text{ m s}^{-1}$
Show that the impulse on the ball has magnitude 4 N s
[3 marks]
\hfill \mbox{\textit{AQA Further Paper 3 Mechanics 2021 Q3 [3]}}