An object travels horizontally at 15.00 meters per second off a cliff that is 12.00 meters tall. How far from the base of the cliff does the object land?
how long does it take to fall 12m?
Multiply that by 15
h= gt²/2,
t=2h/g=2•12/9.8=2.45 s
s=v•t = 15•t=15•2.45 = 36.7 m
To determine how far from the base of the cliff the object lands, you can use the equations of motion.
First, let's find the time it takes for the object to reach the ground. We can use the equation:
h = (1/2) * g * t^2
Where:
h = vertical distance (12.00 meters in this case, as the cliff is 12.00 meters tall)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken
Rearranging the equation to solve for t:
t = √(2h/g)
Plugging in the values:
t = √(2 * 12.00 m / 9.8 m/s^2) ≈ 1.40 seconds
Now that we have the time, we can find the horizontal distance the object travels using the equation:
d = v * t
Where:
d = horizontal distance
v = horizontal velocity (15.00 meters per second in this case)
t = time
Plugging in the values:
d = 15.00 m/s * 1.40 s ≈ 21.0 meters
Therefore, the object lands approximately 21.0 meters from the base of the cliff.