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 of 95.0 cm/s. How far from the base of the cliff will Milada hit the ground?
ey boss
To find the horizontal distance from the base of the cliff where Milada will hit the ground, we can first find the time it takes for her to reach the ground.
We are given Chirpy's time to reach the ground, which is 3.50 s.
Since both crickets start from the same initial height, and Chirpy just drops, we can assume the vertical distance traveled by both crickets is the same.
Using the equation of motion for free fall:
s = ut + 0.5 * a * t^2
Where:
s = vertical distance traveled
u = initial vertical velocity (for Chirpy, this is 0)
t = time taken (3.50 s)
a = acceleration due to gravity (-9.8 m/s^2)
For Chirpy:
s = 0 * 3.50 + 0.5 * (-9.8) * (3.50)^2
s = -0.5 * 9.8 * (3.50)^2
s = -0.5 * 9.8 * 12.25
s = -0.5 * 120.05
s ≈ -60.03
Since we are only interested in the magnitude of the distance, we can take the absolute value of s, which is approximately 60.03 m.
Now, we can use this distance to calculate the time taken for Milada to reach the ground horizontally.
Since the only force acting on her is gravity (in the vertical direction), there is no horizontal acceleration. Therefore, the horizontal speed remains constant throughout her motion.
Using the equation for horizontal motion:
s = u * t
Where:
s = horizontal distance traveled (we'll call it d)
u = initial horizontal velocity (95.0 cm/s or 0.95 m/s)
t = time taken to reach the ground
For Milada:
d = 0.95 * t
Now, we can solve for t:
t = d / 0.95
Substituting the value of d, we have:
t = 60.03 / 0.95
t ≈ 63.18 s
Therefore, Milada will hit the ground approximately 63.18 s after jumping.
To determine how far from the base of the cliff Milada will hit the ground, we can use the horizontal velocity and time of flight.
Given:
Initial horizontal velocity (Vx) = 95.0 cm/s,
Time of flight (t) = 3.50 s.
Since the initial horizontal velocity is constant, we can use the equation:
Distance = Velocity x Time
To find the distance, we need to calculate the horizontal distance traveled by Milada. Since there is no horizontal acceleration, the horizontal velocity remains constant throughout the motion.
Therefore, the horizontal distance (d) traveled by Milada can be calculated by multiplying the horizontal velocity (Vx) by the time of flight (t):
Distance = Velocity x Time
d = Vx * t
Substituting the given values:
d = 95.0 cm/s * 3.50 s
Calculating the final answer:
d = 332.5 cm
Therefore, Milada will hit the ground approximately 332.5 cm (or 3.325 m) away from the base of the cliff.