You accidentally throw your car keys horizontally at 10.0 m/s from a cliff 54 m high. How far from the base of the cliff should you look for the keys?
some accident ...
you need the flight time
... zero is on the ground, 54 is starting height
... remember gravitational acceleration is downward
0 = 1/2 g t^2 + 54 ... 0 = -4.9 t^2 + 54
solve for t (flight time)
... multiply by 10 m/s to find the distance
To determine how far from the base of the cliff you should look for the keys, we can use kinematic equations to find the horizontal distance the keys will travel before hitting the ground.
First, let's analyze the given information:
Initial velocity (horizontal): 10.0 m/s
Initial height: 54 m
We can ignore air resistance in this case.
To find the time of flight, we can use the kinematic equation for vertical motion:
h = ut + (1/2)gt^2
Where:
h = vertical displacement (54 m)
u = initial vertical velocity (0 m/s)
g = acceleration due to gravity (-9.8 m/s^2)
t = time of flight
54 = 0 + (1/2)(-9.8)t^2
54 = -4.9t^2
t^2 = 54 / -4.9
t^2 ≈ -11.02
Since time cannot be negative, it means the keys will take some time to hit the ground. This negative result suggests that the keys will not hit the ground at all.
Therefore, we cannot determine the exact distance from the base of the cliff where you should look for the keys, as they will not reach the ground horizontally.