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Maths
A Level
A ball is thrown from ground level at an angle of 30 degrees from the horizontal with a velocity of 20 m/s. It just clears a wall with a height of 5m, from this calculate the distances that the wall could be from the starting position.
The first thing to do is draw a diagram to visualise the problem. Next we write down all the information the question gives us as well as which values we want to find. For this question it would be
Find dy/dx at t=3, where x=t^3-5t^2+5t and y=2t^2
Using the product rule, we find that dy/dx= dy/dt multiplied by dt/dx, where dt/dx is the reciprocal of dx/dt
dx/dt= 3t^2-10t+5, dy/dt= 4t
At t=3, dx/dt= 3(3)^2-10(3)+5=2, dy/dt= 4(3)= 12
