Using derivatives to compute velocity if only displacement is given

calculuschain rulederivativesprojectile motion

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