a cannon is 80 feet long. the muzzle velocity = 960 ft / sec. if fired strait up, what is the maximum height

the equation for the height is

h = 80 + 960t - 16t^2

As you recall, the vertex (maximum height) is at t = 960/32 = 30

Now just figure h(30)

Well, if the cannonball is fired straight up, it'll probably hit a bird or two on its way down. But let's calculate the maximum height first! Now, to determine the maximum height, we can use the equation:

Max Height = (Initial Velocity)^2 / (2 * Gravity)

Since we know the initial velocity is 960 ft/sec and gravity is around 32 ft/sec^2, let's plug in the values:

Max Height = (960^2) / (2 * 32) = 28,800 / 64 = 450 feet

So, if my calculations aren't completely ballistic, the maximum height the cannonball will reach is approximately 450 feet. Just watch out for any startled birds on its way down!

To find the maximum height reached by the cannonball when fired straight up, we can use the equation of motion for vertical motion.

The initial velocity in the upward direction is the muzzle velocity, which is 960 ft/s. The final velocity at the highest point is zero since the cannonball momentarily stops before falling back down.

Using the equation v² = u² + 2as, where v = final velocity, u = initial velocity, a = acceleration, and s = displacement, we have:

0² = (960 ft/s)² + 2a * s

Rearranging the equation, we get:

a * s = - (960 ft/s)²

Since the acceleration due to gravity is -32 ft/s² (negative because it acts in the opposite direction of the initial velocity), we can substitute it in for 'a':

(-32 ft/s²) * s = - (960 ft/s)²

Simplifying further:

s = (960 ft/s)² / (32 ft/s²)

s = 29,760 ft²/s² / 32 ft/s²

s = 930 ft

So, the displacement or maximum height reached by the cannonball is 930 feet.

To calculate the maximum height reached by the cannonball when fired straight up, we first need to understand the basic principles of projectile motion.

In projectile motion, an object is launched at an initial velocity and follows a curved path under the influence of gravity. When a cannonball is fired straight up, the initial velocity (muzzle velocity) is considered positive, while the acceleration due to gravity is considered negative.

The key concept to find the maximum height is that at the highest point of the trajectory, the vertical component of the velocity becomes zero. Using this information, we can calculate the time taken to reach the maximum height. Let's break down the problem:

1. Find the time it takes for the cannonball to reach its maximum height:
Since acceleration due to gravity is constant, we can use the equation:
v = u + at
Here, v is the final velocity (which is 0 when the cannonball reaches the maximum height),
u is the initial velocity (muzzle velocity),
a is the acceleration due to gravity (approximately -9.8 m/s^2),
t is the time taken.

Rearranging the equation, we get:
t = (v - u) / a

Plugging in the given values:
t = (0 - 960) / -9.8

2. Calculate the maximum height:
Once we have calculated the time taken to reach the maximum height, we can use the equation:
s = ut + (1/2)at^2
Here, s is the displacement (maximum height),
u is the initial velocity (muzzle velocity),
t is the time taken,
a is the acceleration due to gravity.

Rearranging the equation, we get:
s = ut + (1/2)at^2
s = 960t + (1/2)(-9.8)t^2

Plugging in the calculated value of "t" from step 1:
s = 960 * [(0 - 960) / -9.8] + (1/2)(-9.8) * [(0 - 960) / -9.8]^2

Simplifying the equation will give you the maximum height reached by the cannonball.