# Projectile Problem - Time of Peak

• courtney1121
In summary, the equation t=v0z/g can be used to calculate the time it takes for a fireworks rocket to reach its peak if it has an initial upward speed of 58 m/s when launched. The angle is not necessary when the trajectory is parallel with the deceleration vector, and the time would be 5.9 seconds in this case. However, if the angle is specified, the time would vary accordingly. The equation assumes that there is no thrust and only gravity is decelerating the rocket.
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?

Anyone have an idea?

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.

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

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

## 1. What is the "time of peak" in a projectile problem?

The "time of peak" in a projectile problem refers to the moment when the projectile reaches its maximum height or distance. This is also known as the "apex" or "vertex" of the projectile's trajectory.

## 2. How is the time of peak calculated in a projectile problem?

The time of peak can be calculated using the formula t = -b/2a, where t represents time, b represents the vertical component of initial velocity, and a represents the vertical acceleration due to gravity. Alternatively, the time of peak can be found by using the formula t = v0/g, where v0 represents the initial vertical velocity and g represents the acceleration due to gravity.

## 3. Can the time of peak be negative in a projectile problem?

Yes, the time of peak can be negative in a projectile problem if the initial vertical velocity is negative and the acceleration due to gravity is positive. This indicates that the projectile reached its maximum height before being launched.

## 4. How does air resistance affect the time of peak in a projectile problem?

In most cases, air resistance will cause the time of peak to occur earlier than it would without air resistance. This is because air resistance acts as a force that slows down the projectile, reducing its vertical velocity and causing it to reach its maximum height sooner.

## 5. Is the time of peak affected by the angle of launch in a projectile problem?

Yes, the time of peak is affected by the angle of launch in a projectile problem. A higher angle of launch will result in a longer time of peak, as the projectile will spend more time in the air before reaching its maximum height. A lower angle of launch will result in a shorter time of peak.

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