the rate of the fall of an object can be determined by the formula h=1/2gt^2 where h is the height, g is the acceleration due to gravity and t is time in seconds. If a gun is fired 5 feet above the ground and level to the ground, how far would the bullet travel if its velocity is 600 ms^-1 (assume no air resistance)
solve for t in
16t^2 = 5
then plug that t into the distance
d = 600t
sorry where did you get 16 from?
g = 32 ft/s^2
ya just gotta know some things
To determine how far the bullet would travel, we need to calculate the time it takes for the bullet to hit the ground using the given formula, and then multiply it by the horizontal velocity of the bullet.
First, we need to find the time it takes for the bullet to hit the ground. We know that the initial height of the bullet is 5 feet, which we can convert to meters (since the formula is derived using SI units):
5 feet = 1.524 meters
Now, let's rearrange the formula to solve for time (t):
h = (1/2) * g * t^2
1.524 = (1/2) * 9.8 * t^2 (acceleration due to gravity, g, is approximately 9.8 m/s^2)
Simplifying the equation:
1.524 = 4.9 * t^2
Divide both sides by 4.9:
t^2 = 0.3106122448979592
Take the square root of both sides to solve for t:
t = √0.3106122448979592 ≈ 0.557 seconds
Now that we have the time it takes for the bullet to hit the ground, we can calculate the horizontal distance it would travel. Using the horizontal velocity of the bullet, which is 600 m/s, we can multiply it by the time (t):
Distance = Velocity * Time
Distance = 600 m/s * 0.557 s
Calculating the result:
Distance ≈ 334.2 meters
Therefore, if the bullet has a velocity of 600 m/s and is fired 5 feet above the ground in a level direction, it would travel approximately 334.2 meters before hitting the ground.