Projectile question-independence?

Question

I know that in a projectile motion, x and y are independent.

I have a problem that only tells me that the river is 75 m wide. I am trying to find the MINIMUM initial speed for the rock to get across the river and the time it is in the air.

Can I use the equation: distance= Vot+(1/2)9.8t^2
for an x component (b/c I only know the distance for x) to get time?

I got 3.9 s

Answer 1

ok my friend
i assume that by now you know that maximum distance is achieved by throwing something at 45 degrees. so start by that and take into consideration that Ux is constant and is Ucos45
so
t = 75 / Ucos45


now at 75meters the Height is zero for Uy component
meaning that

0 =H = Uyt - 1/2gt^2 =>

usin

Usin45 * = 1/2 g * 75/Ucos45 ==>

U = sqrt ( 75*9.81) => U = 27.12 m / sec

i used the fact that time is the same and for Ux the distance is 75 but the same time leads to height zero for Uy.


nou UX = S/t=>
t = 75 /Ucso45*

and t=3.91sec

Answer 2

If the problem asks for the minimum speed, wouldn't that speed be something close to zero? What could possibly be less than that?If you assume a speed without vertical component, then

speed=distance/time

If the speed is close to zero, you will have to wait till eternity before it gets across the river, but it will get there. Look at this formula:

time=distance/speed

When speed is close to zero, time equals infinity.