A symmetric projectile spends a total of 20 seconds in the air. It reaches a peak height of 8 meters. HOw long it takes to reach its peak height? The projectile has a range of 80 meters.What is its horizontal velocity? What is the projectile's horizontal acceleration? What is the projectile's vertical acceleration?

Tr = 20/2 = 10 s. = Rise time.

Range = Xo * T = 80 m.
Xo * 20 = 80
Xo = 4 m/s = Hor. component of initial
velocity.

a = 0 = Hor. acceleration.

a = g = 9.81 m/s^2. = Ver. acceleration.

To find the time it takes for the projectile to reach its peak height, we can use the fact that the motion of the projectile is symmetric. This means it will take half of the total time for the projectile to reach its peak height.

Step 1: Find the time it takes for the projectile to reach its peak height.
The total time in the air is 20 seconds, so the time to reach the peak height is half of that:
Time to reach peak height = 20 seconds / 2 = 10 seconds.

To find the horizontal velocity of the projectile, we can use the formula for range, which is given by:
Range = Horizontal velocity x Time of flight.

Step 2: Find the horizontal velocity.
The range of the projectile is 80 meters, and the time of flight is 20 seconds. Rearranging the formula, we can solve for the horizontal velocity:
Horizontal velocity = Range / Time of flight = 80 meters / 20 seconds = 4 meters per second.

The horizontal acceleration of the projectile is zero because there is no change in horizontal velocity throughout its flight.

The vertical acceleration of the projectile can be calculated using the formula for the time to reach maximum height:
Vertical acceleration = (2 x Maximum height) / (Time to reach peak height)².
Substituting the values, we get:
Vertical acceleration = (2 x 8 meters) / (10 seconds)² = 16 meters per second squared.

So, to summarize:
- The projectile takes 10 seconds to reach its peak height.
- The horizontal velocity of the projectile is 4 meters per second.
- The horizontal acceleration of the projectile is 0 meters per second squared.
- The vertical acceleration of the projectile is 16 meters per second squared.