A projectile is shot from the ground at a velocity of #1 ms^-1# at an angle of #pi/3#. How long will it take for the projectile to land?

Rearranging to make the time the subject:

This makes sense as an answer due to the very low initial velocity.

To find the time it takes for the projectile to land, you can use the equation for the time of flight of a projectile:

$T = \frac{2 \times V_0 \times sin(\theta)}{g}$

where:

• $T$ is the time of flight,
• $V_0$ is the initial velocity (1 m/s in this case),
• $\theta$ is the launch angle ($\pi/3$ radians in this case),
• $g$ is the acceleration due to gravity (approximately $9.81 \, m/s^2$).

Plugging in the values:

$T = \frac{2 \times 1 \times sin(\pi/3)}{9.81}$

$T \approx \frac{2 \times 1 \times \sqrt{3}/2}{9.81}$

$T \approx \frac{\sqrt{3}}{9.81}$

$T \approx 0.277 \, seconds$

So, it will take approximately 0.277 seconds for the projectile to land.