# Problem: 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. The height from which the arrow is shot is 6 m. Use g=9.8m/s2 for the magnitude of the acceleration due to gravity.Part AFind ta, the time that the arrow spends in the air.Part BHow long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree?

###### FREE Expert Solution

The range, R is expressed as:

$\overline{){\mathbf{R}}{\mathbf{=}}\frac{{{\mathbf{v}}_{\mathbf{0}}}^{\mathbf{2}}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{\left(}\mathbf{2}\mathbf{\theta }\mathbf{\right)}}{\mathbf{g}}}$

Time of flight of a projectile projected with some angle above the ground:

$\overline{){\mathbf{T}}{\mathbf{=}}\frac{\mathbf{2}{\mathbf{v}}_{\mathbf{0}}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{\theta }}{\mathbf{g}}}$

We'll use the kinematic equation:

Part A

We need to use the equation for the time of flight, but we don't have v0. We can find v0 from the expression for range as:

$\begin{array}{rcl}{\mathbf{v}}_{\mathbf{0}}& \mathbf{=}& \sqrt{\frac{\mathbf{R}\mathbf{g}}{\mathbf{sin}\mathbf{\left(}\mathbf{2}\mathbf{\theta }\mathbf{\right)}}}\\ & \mathbf{=}& \sqrt{\frac{\mathbf{\left(}\mathbf{220}\mathbf{\right)}\mathbf{\left(}\mathbf{9}\mathbf{.}\mathbf{8}\mathbf{\right)}}{\mathbf{sin}\mathbf{\left[}\mathbf{\left(}\mathbf{2}\mathbf{\right)}\mathbf{\left(}\mathbf{45}\mathbf{°}\mathbf{\right)}\mathbf{\right]}}}\end{array}$

v0 = 46.43 m/s

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###### Problem Details

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. The height from which the arrow is shot is 6 m. Use g=9.8m/s2 for the magnitude of the acceleration due to gravity.

Part A

Find ta, the time that the arrow spends in the air.

Part B

How long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree?