# A bullet is shot horizontally from shoulder height

## 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?

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

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

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