Question

A projectile is shot on level ground with a
horizontal velocity of 11 m/s and a vertical
velocity of 21 m/s.
Find the time the projectile is in the air.
The acceleration due to gravity is 9.8 m/s
2
.
Answer in units of s

Answer 1

When anything goes up, it must come down. At the highest point, vertical velocity will be zero. It spends half the time in the air going up and the other half going down, but each of these is equal. So find out how long it takes the projectile that starts at 21 m/s goes to 0 m/s due to the decelerating force of gravity and double it:

$$
v=at+v_0
$$
Where \(v\) is the final velocity (i.e. 0) and \(a=9.8~m/s\) and \(v_0=21~m/s\).

Solve for \(t\), then double it, due to the reasons I just described. That is how long the projectiles spends in the air.