# Math Help - Related Rates

1. ## Related Rates

Hi, I'm having a lot of trouble with this problem. Help would be greatly appreciated

The kinetic energy of amoving object equals half the product of itsmass and the square of its velocity. K = mV^2 As a spaceship is fired into orbit, all three ofthese quantities vary. Suppose that the kineticenergy of a particular spaceship is increasingat a constant rate of 100,000 units per secondand that mass is decreasing at 20 kg/s becauseits rockets are consuming fuel. At what rate isthe spaceship’s velocity changing when itsmass is 5000 kg and it is traveling at 10 km/s?

2. Originally Posted by legolewinsky
Hi, I'm having a lot of trouble with this problem. Help would be greatly appreciated

The kinetic energy of amoving object equals half the product of itsmass and the square of its velocity. K = (1/2)mV^2 As a spaceship is fired into orbit, all three ofthese quantities vary. Suppose that the kineticenergy of a particular spaceship is increasingat a constant rate of 100,000 units per secondand that mass is decreasing at 20 kg/s becauseits rockets are consuming fuel. At what rate isthe spaceship’s velocity changing when itsmass is 5000 kg and it is traveling at 10 km/s?
$K = \frac{1}{2}mv^2$

you are given $\frac{dK}{dt} = 10^5$ u/s

$\frac{dm}{dt} = -20$ kg/s

you are asked to find $\frac{dv}{dt}$ when m = 5000 kg and v = 10 km/s

take the time derivative of K (note that you will have to use the product rule since m and v both vary with time).

sub in your given values and solve for $\frac{dv}{dt}$