Two crickets, Chirpy and Milada, jump from the top of a vertical cliff. Chirpy
just drops and reaches the ground in 3.50 s, while Milada jumps horizontally with an initial speed 95.0 cm/s. How far from the base of the cliff will Milada hit the
ground?
To find the distance from the base of the cliff where Milada will hit the ground, we can first calculate the time it takes for Milada to hit the ground. Since Milada jumps horizontally, the vertical motion of the jump can be ignored. The only force acting on Milada is gravity, which causes a constant acceleration downwards.
We know the initial speed of Milada is 95.0 cm/s, and the acceleration due to gravity is approximately 9.8 m/s^2. Since the initial velocity in the vertical direction is zero, we can use the kinematic equation for linear motion:
d = v₀t + 0.5at²
Where:
d is the distance traveled
v₀ is the initial velocity
t is the time taken
a is the acceleration
Since the initial velocity in the vertical direction is zero, the equation simplifies to:
d = 0.5at²
Rearranging the equation to solve for time:
t = sqrt(2d/a)
Using the given information, we can substitute the values:
t = sqrt(2 * 0 / 9.8)
Therefore, t = 0 seconds.
This implies that Milada falls to the ground instantaneously because she possesses horizontal velocity and no vertical velocity. As a result, the distance from the base of the cliff to Milada's landing point is 0 cm.