You accidentally throw your car keys horizontally at 9.0 m/s from a cliff 72 m high. How far from the base of the cliff should you look for the keys?
15 m
T= sqrt (2*72/9.8)= 3.83
3.83*9.0=34.47m
To determine how far from the base of the cliff you should look for the keys, we can use the kinematic equation for horizontal displacement.
The equation is given by:
d = v * t
Where:
d is the horizontal displacement
v is the initial horizontal velocity
t is the time of flight
In this case, we are given the initial horizontal velocity, which is 9.0 m/s. We need to find the time of flight, which can be determined using the equation:
t = sqrt(2h / g)
Where:
h is the height of the cliff
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Substituting the given values:
h = 72 m
g = 9.8 m/s^2
t = sqrt(2 * 72 / 9.8)
t โ sqrt(14.69)
t โ 3.83 s (approx.)
Now that we have the time of flight, we can calculate the horizontal displacement using the equation:
d = v * t
d = 9.0 m/s * 3.83 s
d โ 34.47 m (approx.)
Therefore, you should look approximately 34.47 meters from the base of the cliff to find your car keys.