An arrow is shot vertically upward and then 2.15 s later passes the top of a tree 37.0 m high. How much longer will the arrow travel upward, and how high will it go?

To find out how much longer the arrow will travel upward, we need to determine the total time it takes for the arrow to reach its maximum height.

From the given information, we know that it takes 2.15 seconds for the arrow to pass the top of the tree. Since the arrow is shot vertically upward, it will take the same amount of time for the arrow to reach its maximum height as it took to pass the top of the tree.

Therefore, the arrow will continue traveling upward for an additional 2.15 seconds.

To determine how high the arrow will go, we can use the equations of motion. Since the arrow is only affected by the force of gravity, we will consider the vertical motion only.

The equation we will use is:

h = ut + (1/2)gt^2

Where:
h = height reached
u = initial velocity
t = time
g = acceleration due to gravity (approximately 9.8 m/s^2)

In this case, the initial velocity (u) is the velocity of the arrow when it was shot upward. However, this information is not provided, so we cannot determine the exact height reached by the arrow.

If we assume that the arrow is shot upward with an initial velocity of 0 m/s (assuming no initial velocity), we can calculate the maximum height reached by the arrow using the equation:

h = (1/2)gt^2

h = (1/2)(9.8 m/s^2)(2.15 s)^2

h ≈ 22.32 m

Therefore, assuming no initial velocity, the arrow will reach a height of approximately 22.32 meters. However, if the initial velocity is given, we can calculate the exact height reached.

Keep in mind that in reality, the arrow would have an initial velocity, so the actual height reached by the arrow will likely be different from the calculated approximate value.