cchapman said:
I was a little dubious of the question, but none of the other answers seemed to fit intuitively and I couldn't be bothered with the physics of it at the time. Since you questioned it, I have calculated it using physics (I'm sure this was a maths test?!) and indeed the answer is correct (or both the BBC and I are wrong.)
Code:
From Newton's second law, f=ma.
The mass of the tennis ball assumedly remains constant.
Therefore to double the force we need to double the acceleration.
In the first case:
displacement s=40
time t=26
acceleration a is unknown
assume initial velocity u=0
Substitute into s=ut+1/2at^2:
40=0+1/2*a*26^2
40=338a
a=40/338
Now for the second case:
s=80
acceleration has doubled so a=2*(40/338)
t is unknown
assume u=0.
Substitute in to s=ut+1/2at^2:
80=0+1/2*80/338*t^2
t^2=80/(1/2*80/338)
t=[80/(1/2*80/338)]^1/2
t=26(OK, I used a calculator for the last bit
)
