a gun shoots a potato from a height of 6 feet. how long does it take to hit the ground.
To determine how long it takes for the potato to hit the ground when shot from a height of 6 feet, we need to consider the acceleration due to gravity and the initial velocity of the potato.
The acceleration due to gravity, g, is approximately 32.2 feet per second squared. Assuming we neglect air resistance, the potato will experience a constant acceleration downward.
We can use the kinematic equation for vertical motion to determine the time it takes for the potato to hit the ground:
d = vit + (1/2)at^2
Where:
d is the vertical distance traveled (in this case, 6 feet)
vi is the initial vertical velocity (which is 0 since the potato is stationary initially)
a is the acceleration due to gravity (-32.2 ft/s^2, negative since it's downward)
t is the time taken
Plugging in the given values, we have:
6 = 0*t + (1/2)(-32.2)t^2
Simplifying, we get:
3 = -16.1t^2
Dividing both sides by -16.1, we have:
t^2 = -3 / (-16.1)
t^2 ≈ 0.18634
Taking the square root of both sides, we find:
t ≈ 0.431 seconds
Therefore, it takes approximately 0.431 seconds for the potato to hit the ground.