1. Its raining and your trying to decide whether or not to run or walk. If you walk you'll spend longer in the rain, but if you run you'll be running into the rain and potentially get wetter. The rain is falling with a velocity of v'rain which has both an x-component as it blows sideways and a y-component as it falls.
You move with a velocity of v'you which only has an x-direction. If the rain is falling with a density ρ and you have a top area of Atop (which rain will fall onto) and a sideways area of (which rain will fall onto if it blows sideways or you move sideways into it), find an expression for how wet you would be when traveling a distance d, as a function of your velocity.
2. The range equation can only be used if the projectile is launched from the ground and returns to the same height as it was fired from. What if instead it was fired from a given height, h?
a) Find the range of an object fired from a height h and at an angle θ.
b) Find the angle of launch which maximizes the range as a function of height.
3. A skateboarder in a death-defying stunt decides to launch herself from a ramp on a hill. The skateboarder leaves the ramp at a height of 1.4 m above the slope, traveling 15 m s-1 and at an angle of 40o to the horizontal. The slope is inclined at 45o to the horizontal.
a) How far down the slope does the skateboarder land?
b) How long is the skateboarder in the air?
c) With what velocity does the skateboarder land on the slope?