An arrow is shot at an angle of θ=45∘ above the horizontal. The arrow hits a tree a horizontal distance D=220m away, at the same height above the ground as it was shot. Use g=9.8m/s2 for the magnitude of the acceleration due to gravity.

1) Find ta, the time that the arrow spends in the air.
Answer numerically in seconds, to two significant figures.

2) Suppose someone drops an apple from a vertical distance of 6.0 meters, directly above the point where the arrow hits the tree.

Please show work. Thank You.

Question

An arrow is shot at an angle of θ=45∘ above the horizontal. The arrow hits a tree a horizontal distance D=220m away, at the same height above the ground as it was shot. Use g=9.8m/s2 for the magnitude of the acceleration due to gravity.

1) Find ta, the time that the arrow spends in the air.
Answer numerically in seconds, to two significant figures.

2) Suppose someone drops an apple from a vertical distance of 6.0 meters, directly above the point where the arrow hits the tree.

Please show work. Thank You.

anonymous · Answer

I suggest the following...

Using these two kinematic equations:$$(1)x=v_{0x}t$$$$(2)y=y_{0}+v_{0y}t-\frac{1}{2}gt^2$$
And the following statements from the problem:$$y=y_{0}$$$$v_{0x}=v_{0}\cos\theta$$$$v_{0y}=v_{0}\sin\theta$$$$\theta = 45$$
Solve equation (2) for time 't'.
Then substitute that expression for 't' into equation (1) and solve for v0.

After solving for v0, you'll find it trivial to plug it back into equation (1) to solve for the time of flight.

autogenius · Answer

Thanks, but I got a really weird number (576 seconds) after I did everything.

autogenius · Answer

Is there any other way I can do this problem?

perl · Answer

*

autogenius · Answer

Thanks, I finally understood how to do it.