Question
A bullet is shot horizontally from shoulder height (1.5 m) with an initial speed of 200 meters per second.
(a) How much time elapses before the bullet hits the ground?
(b) How far does the bullet travel horizontally?
Answer
The answer to a is 0.553 seconds
While for b, the answer is 110.6 meters
Explanation
Data
We will need to identify our data from the question
The height, h = 1.5 m
Horizontal velocity, v = 200 m/s
Initial velocity, u = 0
Acceleration due to gravity, g = 9.8 ms-2
Answer to a
To find out how much time elapses before the bullet hits the ground, we will follow the method below:
Unknown
Elapsed time before the bullet hits the ground, t = ?
Formula
We will apply the formula,
h = ut + (1/2)at2
Since the initial velocity, u = 0
We can rewrite h = ut + (1/2)at2 into
h = (1/2)at2
We can now make t subject of the formula
at2 = 2h
t = √(2h/a)
but we are dealing with the force of gravity, which implies a = g
Thus
t = √(2h/g)
Therefore, to find the elapsed time (t), we will use the formula t = √(2h/g)
Solution
To find the elapsed time, we will now substitute our formula with our data
t = √(2h/g) = √((2 x 1.5) / 9.8)
Which implies that
t = √(3 / 9.8) = √0.306 = 0.553 seconds
Therefore, the elapsed time before the bullet hits the ground is 0.553 seconds
Answer to b
Unknown
Distance traveled by the bullet horizontally, s = ?
Formula
Distance traveled by the bullet horizontally, s = horizontal velocity (v) x elapsed time (t)
Solution
We will insert our data into the above formula
s = v x t = 200 x 0.553 = 110.6 m
Therefore, the distance traveled by the bullet horizontally is 110.6 meters
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