I am reading about the Chain Rule of derivative and encountered this problem:
If a ball is flying at an angle of π/4, what is the required velocity so it will reach 40 foot high and 350 feet horizontal distance?
The given displacement function is:
x(t) = v.cos($\theta$).t
y(t) = v.sin($\theta$).t-(16t$^2$)
Where t is time in second and v is the initial velocity.
I couldn't figure out where to start. I tried solving for t as the time when ball reaches the maximum height but I am stuck there.
Best Answer
You have that $\theta$= $\pi$/4 So you can get the cosine and sine So you just have to put that:
x(t) = v.cos($\theta$).t=350
y(t) = v.sin($\theta$).t-(16t$^2$)=40
And solve these 2 equations in 2 unknowns to get v and t