Question

An archer aims his arrow directly at an orange hanging on an orange tree. At the moment he releases the arrow, the orange drops off the tree. Would the arrow hit the orange? You need to show your work to justify your argument.

Answer 1

Answer:

Yes it would

Explanation:

As the arrow and the orange are in the same position initially, vertically speaking. They are also subjected to the same gravitational acceleration g only in the vertical direction. They also start their motion at the same time. So their equation of motion can be written as

$y = h + gt^2/2$

Where h is the initial height of both of them. Since their g, h, and t are the same, their vertical position must be the same at the same time. As the arrows progress horizontally, it would hit the orange.

Answer 2

Answer:

Yes. In this problem the two bodies are always in projectile motion: the arrow and the orange. The arrow and the orange have different initial positions and velocities, but they go into projectile motion at the same time. In order to show that the arroow always hit the orange, we have to prove that the arrow and orange have the same position along the x and y axis. See attachment.

Explanation: