Question

You run a race with your friend. At first you each have the same kinetic energy, but then you find that she is beating you. When you increase your speed by 28%, you are running at the same speed she is. If your mass is 86 kg, what is her mass?

Answer 1

52.49 Kg

Step-by-step explanation:

Let m1 and v1 denote your mass and velocity respectively

Let m2 and v2 denote your friends mass and velocity respectively

Kinetic energy is given by

`KE= 0.5mv^(2)`

Since your kinetic energies are the same hence

`0.5m1(v1)^(2)=0.5m2(v2)^(2)`

`m1(v1)^(2)=m2(v2)^(2)` and making m2 the subject then

`m2=\frac { m1(v1)^(2)}{(v2)^(2)}`

Since v2 is v1+0.28v1=1.28v1

Substituting m1 for 86 Kg

`m2=\frac { 86 Kg(v1)^(2)}{(1.28v1)^(2)}= 52.49023\approx 52.49 Kg`