If Wile E. Coyote runs of a cliff at a speed of 43 mph and the cliff is 2,100 meters tall, how long will it take for Wile E. Coyote to reach the ground?

Answer 1

Assuming there is no air resistance, we can use the kinematic equation of motion to determine the time it will take for Wile E. Coyote to reach the ground. The relevant equation is:

h = 1/2 * g * t^2 + v0 * t

where:

1. h is the height of the cliff (2,100 meters)
2. g is the acceleration due to gravity (9.8 m/s^2)
3. t is the time it takes for Wile E. Coyote to reach the ground (what we're solving for)
4. v0 is the initial velocity (43 mph or 19.26 m/s)

First, we need to convert Wile E. Coyote's initial velocity to meters per second:

19.26 m/s

Then, we can plug in the values and solve for t:

2,100 m = 1/2 * 9.8 m/s^2 * t^2 + 19.26 m/s * t

Simplifying:

2,100 m = 4.9 m/s^2 * t^2 + 19.26 m/s * t

0 = 4.9 m/s^2 * t^2 + 19.26 m/s * t - 2,100 m

Using the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 4.9 m/s^2, b = 19.26 m/s, and c = -2,100 m

t = (-19.26 ± sqrt(19.26^2 - 4(4.9)(-2,100))) / 2(4.9)

t = (-19.26 ± sqrt(376,250.44)) / 9.8

t ≈ 45.43 s or t ≈ -8.84 s (discarded as irrelevant)

Therefore, it will take Wile E. Coyote approximately 45.43 seconds to reach the ground.