 It's a beautiful day you're out on your bicycle riding at your favorite velocity of five meters per second. When all of a sudden what's that 35 meters ahead of me? It's a mosquito and that mosquito is also moving towards me at a velocity of negative 15 meters per second. So the question is how far from your original starting position are you going to hit that mosquito? I've always loved this question because it allows us to solve a problem using a couple of different methods both of them you actually learned about back in science 10 and math 10c. The first method we're going to take a look at is a graph. Let's make a displacement versus time graph. In this graph I'll be at the pink dot moving forwards at five meters per second and the mosquito will be the blue dot moving backwards at negative 15 meters per second and the key to remember here is those velocities are going to be the same as the slope on the displacement time graph. So where should I start? I think I'll start off at the origin zero meters and zero seconds and I'll scale the y-axis in increments of five meters. The mosquito is going to start off 35 meters up on the y-axis and this is a key idea to the problem as well. If I start 35 meters away from the mosquito that gives the mosquito a wide intercept of 35. Now let's make a graph of my uniform motion. After one second I'll have moved five meters. That line that I just drew has a slope of five meters per second which is the same as my velocity. After two seconds I guess I'll move a total of 10 meters. So now I've got a line that represents my motion. What about the mosquito? Mosquito has a negative velocity. That means it moves down 15 meters in the first second and down another 15 meters in the second second. Now we have this interesting intersection point where the two lines cross is the position in time and space where I'm going to hit the mosquito. So it's about 1.75 seconds and I can tell from my graph it's eight ish meters. I can't exactly get that decimal place which is a little unsatisfying. I'd like to be able to know exactly how many meters from my starting position I hit the mosquito. So there's another method we could use if we're looking for a little bit more accuracy. Think of the equations of these two lines. I would have an equation of y equals 5x because my slope was five meters per second and I didn't have a wide intercept and the mosquito would have an equation of y equals negative 15x plus 35. These equations are in slope wide intercept form which you'll remember from back in math 10c. You'll also remember you did a whole unit on this idea called systems of equations. This concept that if you have two equations which are solved for the exact same variable you can make those two equations equal to each other, cancel out one of the variables and solve for the last one. So that's what we're going to do here. I've got negative 15x plus 35 equals 5x. I'll add 15x to both sides getting 35 equals 20x. I'll divide both sides by 20 to get the value of x as being 1.75. Once I round it to two significant digits that gives me a time of collision of 1.8 seconds. One of the other cool things about systems of equations is once you know the x variable getting the y variable is easy. We just substitute the x back into one of the original equations. Either one will give the same answer and in this case our y variable of 8.75 meters is how far I go before I hit the mosquito. 8.8 meters to two sig sticks. I hope this video helped. For more problems and videos like this one please check out my website LDindustries.ca