Question

In a relay race, runner a is carrying the baton and has a speed of 2.60 m/s. When he is 25.0 m behind the starting line, runner b starts from rest and accelerates at 0.0600 m/s 2. How long afterwards will a catch up with b to pass the baton to b

Answer 1

A will take 11.02 seconds or 75.65 seconds to catch up with B.

Step-by-step explanation

Runner A is carrying the baton and has a speed of 2.60 m/s . So,
`v= 2.60`

When A is 25.0 m behind the starting line, runner B starts from rest and accelerates at 0.0600 m/s². So,
`d_(0)= 25.0` and
`f= 0.0600`

Suppose, A will catch up with B to pass the baton to B after
`t` seconds.

Formula need to use here :
`d= (1)/(2)ft^2 -vt+d_(0)`

When A will catch up with B , then
`d=0`

So, the equation will be .......

`0=(1)/(2)(0.0600)t^2 -(2.60)t+25.0\\ \\ 0=0.03t^2 -2.6t+25`

Using quadratic formula, we will get.....

`t= (-(-2.6)+/-√((-2.6)^2 -4(0.03)(25)))/(2(0.03))\\ \\ t= (2.6+/-√(6.76-3))/(0.06) \\ \\ t= (2.6+/-1.939)/(0.06)\\ \\ t= 75.65, 11.02`

So, A will take 11.02 seconds or 75.65 seconds to catch up with B.