Projectile Problem - Time of Peak

[courtney1121]

If a fireworks rocket has an initial upward speed of 58 m/s when launched, for how long will it coast before reaching its peak?

So could I use the equation t=v0z/g?

When I use this I get the peak to be 5.9s. Is v0z = 58 m/s or would that be 0? Am I approaching this correctly?

 

[courtney1121]

Anyone have an idea?

 

[Xiju]

well you need an angle because time would depend on the angle you use. For example if you launched the rocket at a 50 degree angle the time to reach its peak would be 58sin50 / 9.81 = 4.42 secs. But if you launched the rocket at a 70 degree angle it would be 58sin70 / 9.81 = 5.55 seconds. So you would have to specify the angle.

 

[courtney1121]

oh ok, so even if you shoot the firework straight up, it still needs an angle?

 

[Xiju]

well straight up it would be 90 degrees. 58sin 90 / 9.81 = 5.912 seconds.

 

[Astronuc]

An initial upward speed of 58 m/s when launched implies v0z = 58 m/s, and one does not need an angle since the trajectory is parallel with the deceleration vector.

The equation t=v0z/g is correct assuming that there is not thrust and only gravity is decelerating the rocket.

http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

Vertical launch - http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra1