Two pellets are fired simultaneously from the horizontal, one is fired vertically at 100m/s and the other is fired at 200m/s at an angle theta from the horizontal. Calculate the angle of the second pellet if they both land at the same time.
For this problem, we can look at the two pellets individually. If we find the time taken for the first bullet to reach the ground again, then we know that it must take the same time for the second bullet to land. Once we know this, we can work out the angle at which the second bullet was fired. We also only need consider SUVAT equations for the vertical direction, as we are not worried with how far away the bullets are when they land.
We know the first pellet lands where it was fired from (S=0, U=100 and A=-10) so we can substitute values in to S=UT+0.5AT2, re-arrange and solve to give a time of 10s. The second bullet has a vertical component and a horizontal component to its initial velocity; the vertical component being 200sin(theta). We can then substitute this time and velocity into a second SUVAT for the other pellet (S=0, T=10, A=-10 and U=200sin(theta)). Re-arranging S=UT+0.5AT2 and solving shows that sin(theta) = 0.5 so we can inverse this on the calculator to give Theta = 30 degrees.
