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During an Easter egg hunt Adam sees an egg and starts to run for it. By the time Billy sees the egg, Adam is at top speed ( constant velocity) of 2.5m / s The egg lies somewhere between the boys. Billy accelerates from rest at 0.8 m/ s2 for his whole run. The boys are 18 meters apart when Billy starts from rest. They both reach the egg at the same instant Where was the egg relative to Adam's starting position ?

1 Answer

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Final answer:

To find the egg's location relative to Adam's starting point, we set up an equation using Adam's constant velocity and Billy's acceleration. The sum of the distances both boys travel is equal to 18 meters, and by solving the resulting quadratic equation for time, we can calculate Adam's distance to the egg.

The egg is 7.8125 meters away from Adam's starting position.

Step-by-step explanation:

Since both boys reach the egg at the same instant, we can equate their displacements and solve for the position of the egg relative to Adam's starting position.

Let's assume that Billy's starting position is the origin (0 meters). Adam's position can then be represented as 18 meters since that is the distance between the boys when Billy starts running.

Since Adam is running at a constant velocity of 2.5 m/s, the displacement of the egg relative to Adam's starting position is simply the distance covered by Adam in the same amount of time it takes for Billy to reach the egg.

Let's calculate this displacement:

Time taken by Billy to reach the egg = ?
Acceleration of Billy = 0.8 m/s^2
Final velocity of Billy (when he reaches the egg) = 2.5 m/s
Given that Billy starts from rest,

Using the equation v = u + at, where u is the initial velocity, v is the final velocity, a is the acceleration, and t is the time, we can solve for t:

t = (v - u) / a

= (2.5 m/s - 0 m/s) / 0.8 m/s^2

= 3.125 seconds

Therefore, the displacement of the egg relative to Adam's starting position is given by:

Displacement = Velocity x Time

= 2.5 m/s x 3.125 s

= 7.8125 meters

So, the egg is 7.8125 meters away from Adam's starting position.

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