A potato gun shoots a potato horizontally from a height of 5 feet. How long does it take to hit the ground?
Since there is no vertical velocity component initially, that would be the same time it takes a dropped object to fall 5 feet. Use the equation
5 ft= (g/2)*t^2
where
g = 32.2 ft/s^2
Solve for t.
t = 0.557 s
To find out how long it takes for the potato to hit the ground, we can use the laws of physics. Specifically, we can use the equation for motion under constant acceleration.
Assuming there is no air resistance, the only force acting on the potato is gravity. It causes the potato to accelerate downward at a constant rate of approximately 9.8 meters per second squared (32.2 feet per second squared).
Given that the initial vertical position of the potato is 5 feet, we can use the following equation to find the time it takes for the potato to hit the ground:
y = y0 + v0t + 0.5at^2
Where:
y = final vertical position of the potato (in this case, 0 feet when it hits the ground)
y0 = initial vertical position of the potato (5 feet)
v0 = initial vertical velocity of the potato (0 feet per second, assuming it starts from rest)
t = time taken for the potato to hit the ground
a = acceleration due to gravity (-9.8 m/s^2 or -32.2 ft/s^2)
Plugging in the values, we get:
0 = 5 + 0*t + 0.5*(-32.2)*t^2
Simplifying the equation:
-16.1t^2 + 5 = 0
To solve this equation, we can use the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, a = -16.1, b = 0, and c = 5. Plugging in the values, we get:
t = (0 ± sqrt(0 - 4*(-16.1)*5)) / (2*(-16.1))
Simplifying further, we have:
t = ± sqrt(0 + 322) / (-32.2)
Taking the positive square root:
t ≈ 0.45 seconds
Therefore, it takes approximately 0.45 seconds for the potato to hit the ground when shot horizontally from a height of 5 feet.