I never had a chance to take a physics course in high school and I've been trying to get into it over the last couple of weeks.
I've been at this problem for a couple of days, but I can't seem to break through. I suppose I could just look at the answer and explanation in the back of the book, but if anyone can give me an idea of how I'm supposed to progress here that would be far preferable to having the answer given to me.
A small projectile is launched from the floor at an angle toward a wall.
The distance from the wall is l.
The initial speed is v0.
The angle is theta.
The only force we are considering is gravity.
Find the time it takes for the projectile to reach the wall (t1) and the height (h) where it will impact the wall.
Here's what I've got so far.
Start by separating the x and y components of velocity. Draw a right triangle with vertices A(launch point) B(impact point) C(point where the wall meets the ground).
sin(theta) = opp/hyp = initial vertical velocity / v0
cos(theta) = adj/hyp = initial horizontal velocity / v0
I can rewrite those such that:
initial vertical velocity = (v0)(sin(theta))
initial horizontal velocity = (v0)(cos(theta))
With that, figuring out the time to impact is a piece of cake.
l = (initial horizontal velocity) (t1)
t1 = l / (initial horizontal velocity)
t1= l / (v0)(cos(theta))
Now I have to find the height of the point of impact (h).
It feels like it should be easy enough to do, using this equation:
h = (v)(t) + (1/2)(g)(t^2)
But I can't seem to come up with anything nicer than
h = (sin(theta))(l) / (cos(theta)) + (g)(l^2) / 2(v0^2)(cos(theta)^2)
I can't see that I've made any algebraic mistakes, but I also can't believe that that's the equation this book is expecting me to come up with...