Question

Neglecting air resistance, firing a projectile at an angle of ____

degrees will allow it to have the greatest horizontal displacement or ____

First blank answers :
45
60
90

Second blank answer choices:
Height
Trajectory
Range

Answer 1

Neglecting air resistance, firing a projectile at an angle of 45

degrees will allow it to have the greatest horizontal displacement or range.

We can prove this by using the range formula, which is...

`R=(v^2sin(2 \theta))/(g)`

In order to maximize the value R,
`sin(2 \theta)` has to be equal to 1. What values of theta make sine equal 1? In degrees, that would be 90. So if we let θ equal 45 we get....

`R=(v^2sin(2 (45)))/(g) \Longrightarrow R=(v^2sin(90))/(g) \Longrightarrow R=(v^2(1))/(g)`

Thus, the value of R is maximized.