Wiley Coyote has missed the Road Runner once again. This time he leaves horizontally off the edge of the cliff at 25 m/s. If he hits the 400 m from the base of the cliff, how high is the cliff?
The idea is to split the motion into two independent components.
The vertical motion is subject to the acceleration due to gravity, from which we can find the height of the cliff.
The horizontal motion is simply a uniform velocity of 25 m/s. If it reached 400 m from the cliff, it took 400/25=16 seconds to reach the bottom.
Find the height using:
H=ut+(1/2)gt²
where u=initial vertical velocity = 0
t=16 sec.
To determine the height of the cliff, we can use the equations of motion. The motion of Wiley Coyote can be divided into two parts: the horizontal motion and the vertical motion.
First, let's consider the horizontal motion. We know that the horizontal distance traveled by Wiley Coyote is 400 m, and his initial horizontal velocity is 25 m/s. The equation we can use to find the time of flight is:
Distance = Velocity × Time
Rearranging the equation, we have:
Time = Distance / Velocity
Time = 400 m / 25 m/s = 16 seconds.
Now let's move on to the vertical motion. We can use the equation of motion for vertical motion under constant acceleration:
Distance = Initial Velocity × Time + (1/2) × Acceleration × Time^2
In this case, the initial vertical velocity is 0 m/s because Wiley Coyote leaves the cliff horizontally. The acceleration is due to gravity and is approximately 9.8 m/s^2.
The distance Wiley Coyote falls vertically is the height of the cliff we want to find, h. Thus, the equation becomes:
h = 0 × 16 + (1/2) × 9.8 × (16^2)
Simplifying the equation further, we have:
h = (1/2) × 9.8 × (256)
h = 1256 m
Therefore, the height of the cliff is 1256 meters.