Derive a general equation for the time of flight of the banana en route to the monkey in terms of only the velocity, distance, and height
hint: if you are doing everything right, there should be a lot of cancellations resulting in a relatively simple solution
Okay, this is confusing to me. I have looked at projectile equations for time, range, and velocity. However, this question is asking for one equation like T= V, D, H? I am not even sure if this is possible. The graph it gave me contained no numbers just labeled height, velocity, and distance leading me to believe that it wants me to come up with an equation for time that if given velocity, distance, and height you can plug it into that one equation and come up with time. How the heck do I combine 3 separate equations into one? Am I approaching this wrong?
What is the banana doing? What is the monkey doing? Where are they in relation to each other?
the banana is not even on the graph. The monkey is in the tree. It shows a canon and I'm guessing the banana is shot out of that to the monkey.
cannon*
You're not approaching it wrong! The question is asking you to derive a single equation that relates the time of flight of the banana to its initial velocity, distance traveled, and height. This means we need to combine the equations for time of flight, range, and velocity in a way that eliminates all the variables except for velocity, distance, and height.
We can start by using the equation for range (horizontal distance traveled) in terms of initial velocity and time of flight:
R = V * T
Here, R represents the horizontal distance. Next, let's express time of flight, T, in terms of vertical distance traveled, height (H), and initial vertical velocity (Vy). We know that during the projectile's motion, the acceleration in the vertical direction is due to gravity:
H = (1/2) * g * T^2, where g is the acceleration due to gravity.
Rearranging this equation, we can solve for T^2:
2H = g * T^2
Now let's eliminate time of flight, T, from the equation for range (R) using the equation above:
R = V * T
T = sqrt(2H/g)
Substituting the value of T in the equation for R, we have:
R = V * sqrt(2H/g)
Finally, we need to solve for time of flight, T, in terms of velocity (V), distance (R), and height (H). Rearranging the equation, we have:
T = R / (V * sqrt(2H/g))
So, the derived general equation for the time of flight of the banana, given its initial velocity, distance traveled, and height, is:
T = R / (V * sqrt(2H/g))
Now, you can plug in the values for velocity, distance, and height into this equation to calculate the time of flight of the banana.