I know the answer to a problem, but I need to understand it.?

Question

You find yourself on a strange planet, and have rigged a setup with a launcher that is 5 meters off the ground, and the launcher will shoot a projectile with an initial velocity of exactly 4.0 m/s. The projectile travels 4.5 m along the ground. From this, you conclude that free-fall gravitational acceleration on this planet is _______ m/s^2.

The answer is supposed to be 7.9 m/s^2.

When I was finding all of the x and y values, this is what I came up with:

X-direction: displacement = 4.5 m
acceleration: 0 m/s^2
initial & final veloctiy: 2.97 m/s
time: 1.51 seconds

Y-direction: displacement: -5 meters
Initial velocity: -2.67 m/s
time: 1.51 seconds.

I guess its possible that I keep messing up the algebra when trying to find the free fall acceleration, but I think its more likely that I came up with one or more incorrect values for the known information (particularly the inital velocities). I'd greatly appreciate it if someone could enlighten to as to where I'm going wrong.Thanks.

Answer 1

You neglected to say anything about the launcher having an angle to the horizontal. Apparently it's 42 degrees above horizontal.

Assuming that, I see a problem with theY-direction data. If you use displacement as -5 meters, that means you define up as positive. Then initial velocity should be +2.67. Using that I get the right answer. The data you gave would mean the launcher is pointing down 42 degrees.

You should have gone on to an equation looking like
y = Vo*t + (1/2)*a*t^2
where y = -5, Vo =2.67, and t = 1.51