Question

If a projectile fired beneath the water, straight up, breaks through the surface at a speed of 13m/s, to what height above the water will it ascend

Answer 1

The projectile will ascend to a height of 9.9 meters above the water's surface.

Step-by-step explanation:

To find the maximum height above the water, we can use the equations of motion for projectile motion. First, we need to find the time it takes for the projectile to reach the surface of the water. We can use the equation y = v0t + (1/2)at2, where y is the displacement, v0 is the initial velocity, a is the acceleration due to gravity, and t is the time.

Given that the initial velocity is -13m/s (since the projectile is moving in the opposite direction of the acceleration due to gravity), the acceleration due to gravity is -9.8m/s2, and the displacement is 0 (since the projectile breaks through the surface of the water), we can rearrange the equation to solve for t: 0 = -13t + (1/2)(-9.8)t2. By solving this quadratic equation, we find that t = 1.33s or t = 0.

Since the time can't be negative, we discard the t = 0 solution. Therefore, the time it takes for the projectile to reach the surface of the water is t = 1.33s. Now, to find the maximum height above the water, we can use the equation v = v0 + at, where v is the final velocity, v0 is the initial velocity, a is the acceleration, and t is the time.

Using the known values: v = 0m/s (since the projectile comes to a stop at its maximum height), v0 = -13m/s, a = -9.8m/s2, and t = 1.33s, we can rearrange the equation to solve for the maximum height h: 0 = -13 - 9.8(1.33) + h. By solving this equation, we find that h = 9.9m. Therefore, the projectile will ascend to a height of 9.9 meters above the water's surface.

Answer 2

well if you had either the velocity or distance traveled i could tell you. But since you haven't all i can say for sure is that the water slowed the bullet down to 13m/s so lets say you knew the distance you would calculate how many meters it traveled and you would have your answer because in this situation, meters (height) =how many seconds spent going into the air.