Answer:
The coyote crashes 66 m from the base of the cliff.
Explanation:
Hi there!
The equation of the position vector of the Coyote is the following:
r = (x0 + v0 · t + 1/2 · a · t², y0 + 1/2 · g · t²)
Where:
r = postion vector of the Coyote at time t.
x0 = initial horizontal position.
v0 = initial horizontal velocity.
t = time.
a = horizontal acceleration.
y0 = initial vertical position.
g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).
Let's place the origin of the frame of reference at the edge of the cliff so that x0 and y0 = 0.
When the Coyote reaches the ground, the vertical component of its position vector (r1 in the figure) will be equal to -29 m. When the vertical component of the position vector is -29 m, the horizontal component will be equal to the horizontal distance traveled by the Coyote (r1x in the figure). So, let's find the time at which the y-component of the position vector is -29 m:
y = y0 + 1/2 · g · t² (y0 = 0)
-29 m = -1/2 · 9.8 m/s² · t²
t² = -29 m / -4.9 m/s²
t = 2.4 s
Now, let's find the x-component of the vector r1 in the figure:
x = x0 + v0 · t + 1/2 · a · t² (x0 = 0)
x = 24 m/s · 2.4 s + 1/2 · 3 m/s² · (2.4 s)²
x = 66 m
The coyote crashes 66 m from the base of the cliff.
