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

Answer:

52.49 Kg

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

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