How much time does a projectile take to land if launched at 20 m/s at a 60° angle?

To determine the time a projectile takes to land when launched, we can use the principles of projectile motion. The total time of flight for a projectile can be calculated using the vertical component of the initial velocity and the acceleration due to gravity.

First, we calculate the vertical component of the initial velocity. The formula to find this vertical component (V_y) when the initial velocity (V) and launch angle (θ) are known is:

V_y = V * sin(θ)

In this case:

• V = 20 m/s

• θ = 60°

Calculating the vertical component:

V_y = 20 m/s * sin(60°) = 20 m/s * (√3/2) ≈ 17.32 m/s

Next, the time of flight can be determined using the formula:

t = (2 * V_y) / g

where g is the acceleration due to gravity, approximately 9.81 m/s². Plugging in the values:

t = (2 * 17.32 m/s) / 9.81 m/s²

Calculating that gives:

t ≈ 3.54 seconds

In the context of the choices given, this time can be rounded