How do I figure out how long it takes two runners to have the same momentum if I am given a, m, and Vi for both runners?
Runner A= 85kg, 2ms-2, Vi=1ms-1
Runner B= 65kg, 3ms-2, Vi=0ms-2
I don't want an answer, just which equations to use or a hint.
momentum is mass times velocity
velocity is ... Vi + (a * t)
write their momenta in terms of t
set the expressions equal, and solve for t
So p=m*Vi + (a*t)
85*1+2t=65*0+3t
85+2t=3t
85=t?
Which is incorrect obviously. I know from other failed methods that the answer is ~3.7seconds.
What am i doing wrong?
To determine how long it takes for two runners to have the same momentum, you can use the equation for momentum, which is given by:
p = m * v
where p is the momentum, m is the mass, and v is the velocity.
In this case, you are given the masses (m) and initial velocities (Vi) for both runners, so you can calculate the initial momenta (pi) for each runner using the equation.
Then, you can set the two momenta equal to each other and solve for the time (t) it takes for the momenta to be equal.
The equation for the momentum of each runner will be:
pA = mA * vA
pB = mB * vB
Setting pA equal to pB:
mA * vA = mB * vB
Now you can plug in the given values for mass and velocity and solve for t:
(85 kg) * (1 m/s) = (65 kg) * (3 m/s)
(take note of the units being properly cancelled out)
Now, to find t, you'll need to rearrange the equation to solve for t:
t = (mB * vB) / (mA * vA)
Using the given values for m and v, substitute them into the equation and solve for t.
Remember, this is just a hint on how to approach the problem. Make sure to double-check all calculations and units to ensure accuracy.