An object with a mass of 49 N falls out of a plane going 20.0 m/s at 300 m above the ground.
1)How do I find the time that the object is in the air?
2)The horizontal distance of the object?
Could someone help me out?
N means Newtons and is FORCE, in this case of gravity (the "weight").
The mass is in KILOGRAMS
and the force 49 N = m g = m (9.8) approximately on earth.
HOWEVER - luckily in this problem all of that matters not at all. It does not matter what the mass or weight is at all. It accelerates downward at 9.8 m/s^2 and keeps going at 20 m/s horizontally.
distance down = (1/2)(9.8) t^2
300 = 4.9 t^2
t = 7.82 seconds in the air
now multiply that by 20.0 m/s to find the horizontal distance.
(Notice that the bomb hits right under the plane if the plane keeps going at 20 m/s straight. Always bank and climb after dropping bombs.)
Certainly! I'd be happy to help you find the time in the air and the horizontal distance traveled by the object.
1) To find the time that the object is in the air, we can use the equation of motion:
h = vi*t + (1/2)*a*t^2
Where:
h = height or vertical distance traveled (300 m in this case)
vi = initial vertical velocity (0 m/s since the object is just released)
a = acceleration due to gravity (-9.8 m/s^2, assuming downward direction)
t = time
We can rearrange this equation to solve for time (t):
300 = 0*t + (1/2)*(-9.8)t^2
0 = (-4.9)t^2 + 0*t + 300
This is a quadratic equation of the form:
at^2 + bt + c = 0
We can solve this equation using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = -4.9, b = 0, and c = 300. Plugging these values into the quadratic formula, we get:
t = (-0 ± √(0^2 - 4*(-4.9)*300)) / (2*(-4.9))
Solving the equation, we find two possible times, one of which is negative (which doesn't make physical sense):
t ≈ 7.75 s
Therefore, the object is in the air for approximately 7.75 seconds.
2) To find the horizontal distance traveled by the object, we can use the equation:
d = v*t
Where:
d = horizontal distance
v = horizontal velocity (20.0 m/s)
Since there is no horizontal acceleration, the horizontal velocity remains constant throughout the motion. Therefore, we can simply multiply the horizontal velocity by the time the object is in the air:
d = 20.0 * 7.75
d ≈ 155 m
Hence, the object will travel approximately 155 meters horizontally.
Let me know if there's anything else I can assist you with!