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Another math question pls help

Two particles A and B have masses m kg and 3 kg respectively,
where m > 3. The particles are connected by a light inextensible string which passes over a smooth, fixed pulley. Initially A is 2.5 m above horizontal ground. The particles are released from rest with the string taut and the hanging parts of the string vertical, as shown in the figure. After A has been descending for 1.25s, it strikes the ground. Particle A reaches the ground before B has reached the pulley.
a Show that the acceleration of B as it ascends is 3.2 m s-2.
b Find the tension in the string as A descends.
c Show that m = 65/11
d State how you have used the information that the string is inextensible.
When A strikes the ground it does not rebound and the string becomes slack. Particle B then moves freely under gravity, without reaching the pulley, until the string becomes taut again.

e Find the time between the instant when A strikes the ground and the instant when the string becomes taut again.

Can someone help with question e please, I keep getting 20/49s but the answer is 40/49s🥲🥲
(edited 3 months ago)
Reply 1
Original post by banana_22xx
Two particles A and B have masses m kg and 3 kg respectively,
where m > 3. The particles are connected by a light inextensible string which passes over a smooth, fixed pulley. Initially A is 2.5 m above horizontal ground. The particles are released from rest with the string taut and the hanging parts of the string vertical, as shown in the figure. After A has been descending for 1.25s, it strikes the ground. Particle A reaches the ground before B has reached the pulley.
a Show that the acceleration of B as it ascends is 3.2 m s-2.
b Find the tension in the string as A descends.
c Show that m = 65/11
d State how you have used the information that the string is inextensible.
When A strikes the ground it does not rebound and the string becomes slack. Particle B then moves freely under gravity, without reaching the pulley, until the string becomes taut again.

e Find the time between the instant when A strikes the ground and the instant when the string becomes taut again.

Can someone help with question e please, I keep getting 20/49s but the answer is 40/49s🥲🥲

It helps to see what you did, but your answer is 1/2 the book answer so guessing you did the time to peak height?
Reply 2
Original post by mqb2766
It helps to see what you did, but your answer is 1/2 the book answer so guessing you did the time to peak height?

Hi, this was my calculation for the question:
u=4 v=0 a =-9.8 and t=?
so v=u+at
0=4-9.8t and so I got t=20/49s as my final answer
Reply 3
Original post by banana_22xx
Hi, this was my calculation for the question:
u=4 v=0 a =-9.8 and t=?
so v=u+at
0=4-9.8t and so I got t=20/49s as my final answer

Thats what I thought. The string does not become taut again when v=0. Thats the peak height. As its a parabola and symmetric about the peak height (turning point), the velocity when it returns to the starting displacement (when the string becomes slack) is v=-u.

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