Crickets Chirpy and Milada jump from the top of a vertical cliff. Chirpy drops downward and reaches the ground in 2.70 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? Ignore air resistance.

Verified step by step guidance

1. Determine the time it takes for Milada to reach the ground. Since both Crickets are subject to the same gravitational acceleration and start from the same height, Milada will also take 2.70 seconds to reach the ground.
2. Convert Milada's initial horizontal speed from cm/s to m/s for consistency in units. Since 1 m = 100 cm, divide the speed value by 100.
3. Use the formula for horizontal displacement, which is given by \(x = v_{0x} \times t\), where \(v_{0x}\) is the initial horizontal velocity and \(t\) is the time of flight.
4. Substitute the converted speed and the time into the displacement formula to calculate the horizontal distance Milada travels before hitting the ground.
5. The result from the calculation will give you the distance from the base of the cliff where Milada lands.

Key Concepts

Free Fall

Free fall refers to the motion of an object under the influence of gravity alone, without any air resistance. In this scenario, Chirpy's downward motion is a classic example of free fall, where the only force acting on him is gravity, causing him to accelerate at approximately 9.81 m/s². The time taken to fall can be used to calculate the height of the cliff.

Projectile Motion

Projectile motion describes the motion of an object that is launched into the air and is subject to gravitational force. Milada's horizontal jump can be analyzed as a projectile motion problem, where she moves horizontally at a constant speed while simultaneously falling vertically due to gravity. The horizontal distance traveled can be calculated using the time of flight and the horizontal velocity.

Kinematic Equations

Kinematic equations are mathematical formulas that describe the motion of objects under constant acceleration. These equations can be used to relate displacement, initial velocity, final velocity, acceleration, and time. In this problem, they are essential for determining the height of the cliff from Chirpy's fall and for calculating the horizontal distance Milada travels before hitting the ground.