Two kittens are running toward each other, one is named Chloe and the other is named Luna. Luna runs at a speed of 1.10 m/s. If Chloe jumps at an angle of 28.0° with speed 2.60 m/s, at what distance from Luna should Chloe jump to make sure she lands on Luna?

To determine the distance from Luna that Chloe should jump to ensure she lands on Luna, we can use the principles of projectile motion.

Let's break down the problem into two components: the vertical and horizontal motions of Chloe.

First, let's calculate the time it takes for Chloe to reach her maximum height. The initial vertical velocity (Vy) can be calculated using the following formula:

Vy = V * sin(θ)
Vy = 2.60 m/s * sin(28.0°)
Vy ≈ 1.19 m/s

Next, we can use the following equation to calculate the time taken to reach maximum height (t_peak):

t_peak = Vy / g
t_peak = 1.19 m/s / 9.8 m/s²
t_peak ≈ 0.122 seconds

Now, we can calculate the total time of flight (t_total), which is the time it takes for Chloe to reach Luna:

t_total = 2 * t_peak
t_total = 2 * 0.122 seconds
t_total ≈ 0.244 seconds

Given that Luna is running at a constant speed of 1.10 m/s, we can calculate the horizontal distance covered by Luna during Chloe's flight:

Horizontal distance (d) = speed * time
d = 1.10 m/s * 0.244 seconds
d ≈ 0.268 meters

Therefore, Chloe should jump at a distance of approximately 0.268 meters from Luna to ensure she lands on Luna.