The closest answer would be C.
The choices given do not give the exact value.
To answer this, you just need to remember the main formula:
Where:
d = distance/displacement
g = acceleration due to gravity
t = time in flight
Vi = initial velocity.
With this formula, you derive all the formulas you need to look for certain components. You need to keep in mind of the following:
---if you are looking for a vertical component(y), you need to use values of vertical motion.
*Viy is always 0m/s at the beginning of a free-fall.
---If you are looking for a horizontal component(x), you need to use values of horizontal motion.
*g is always 0m/s² when taking horizontal motion into account.
--- time is the only value that is both vertical and horizontal.
Okay, let's get back to solving your problem. Let's see what your given is first:
dy = 137m (as long as it refers to height, it is vertical distance)
dx = 4km (the word, far or away usually indicates horizontal distance)
g = 1.63m/s²
The question is how fast was it going
horizontally and we can derive it from our equation:
We use this because x means horizontal. But notice that we do not have time yet. So how are we going to solve this 2 variables missing? The key is that time is a horizontal and vertical component. Whatever time it took moving horizontally, it is the same vertically as well. So we use the vertical formula to derive time:
Now plug in what you know and solve for what you don't know:
The total time in flight is
12.965s.Let's round it off to
13s.
Now that we know that, we can use this in the horizontal formula:
Hold up! Look at the unit of the horizontal distance. It is in km but all our units are expressed in m so we need to convert that first.
1km = 1,000m
4km = 4,000m
Our new horizontal distance is 4,000m.
Okay, let's wrap this up by solving for what is asked for, using all the derived values.
The horizontal velocity is 308m/s.
Such a long explanation I know, but hopefully, you learned from it.
