Crickets Chirpy and Milada jump from the top of a vertical cliff. Chirpy just drops and reaches the ground in 3.10 s , while Milada jumps horizontally with an initial speed of 89.0 cm/s. How far from the base of the cliff will Milada hit the ground? Ignore air resistance.
Your teacher is really trying to get to you with this separation of constant horizontal speed from increasing vertical speed.
89 * 3.10 centimeters if you really mean cm/s
To find the horizontal distance that Milada will hit the ground, we first need to determine the time it takes for Milada to hit the ground.
Since Chirpy simply drops vertically, we can use the equation:
Vertical distance = 1/2 * acceleration * time^2
Since the acceleration due to gravity is constant and we want to find the time it takes for Chirpy to reach the ground, we can rearrange the equation to solve for time:
time = sqrt(2 * vertical distance / acceleration)
Using the given vertical distance of the cliff (which we assume the same for both Chirpy and Milada since they start from the same height), we can calculate the time taken by Chirpy:
time = sqrt(2 * vertical distance / acceleration)
= sqrt(2 * 0 / acceleration)
= 0
This means that Chirpy hits the ground instantaneously, confirming the information given in the question.
Now, let's focus on Milada. Since Milada jumps horizontally with an initial speed, the horizontal distance will be determined by the time she remains in the air.
Since there is no horizontal acceleration, we can use the equation:
Horizontal distance = initial horizontal speed * time
Now, we need to determine the time it takes for Milada to reach the ground. Since we already know that Chirpy hits the ground in 3.10 s, we can assume that Milada takes the same time to reach the ground.
Using the given initial speed of Milada and the time:
Horizontal distance = initial horizontal speed * time
= 89.0 cm/s * 3.10 s
= 275.9 cm
Therefore, Milada will hit the ground approximately 275.9 cm away from the base of the cliff.