Question

A bullet is fired with an initial velocity of 100 m/s at an angle of 30° from the level ground. Determine the amount of time the bullet spends in the air.

Answer 1

In order to calculate the amount of time, first let's calculate the vertical speed of the bullet:

`\begin{gathered} V_y=V\cdot\sin (\theta) \\ V_y=100\cdot\sin (30\degree) \\ V_y=100\cdot0.5 \\ V_y=50\text{ m/s} \end{gathered}`

Since the displacement of the bullet is zero (it starts from the ground and finishes at the ground), let's use the following formula to find the time:

`\begin{gathered} \Delta S=V_0t+(at^2)/(2) \\ 0=50\cdot t+((-9.8)t^2)/(2) \\ 0=50t-4.9t^2 \\ 4.9t^2=50t \\ 4.9t=50 \\ t=(50)/(4.9) \\ t=10.2\text{ seconds} \end{gathered}`