An arrow is shot horizontally at 29.8 m/s from the roof of a building. It hits t

Question

An arrow is shot horizontally at 29.8 m/s from the roof of a building. It hits the ground 2.6 seconds later. Ignore air resistance.

A) What are the initial values of ax and vx?

B) What are the initial values of ay and vy?

C) How tall is the building?

D) How far from the base of the building does the arrow land?

E) What are the horizontal and vertical components of the velocity just before the arrow reaches the ground?

F) What is the angle of the velocity to the horizontal just before the arrow hits the ground?

1. (20 points) An arrow is shot horizontally at 29.8 m/s from the roof of a building. It hits the ground 2.6 seconds later. Ignore air resistance. A) What are the initial values of ax and vx? B) What are the initial values of ay and vy? c) How tall is the building? D) How far from the base of the building does the arrow land? E) What are the horizontal and vertical components of the velocity just before the arrow reaches the ground? F) What is the angle of the velocity to the horizontal just before the arrow hits the ground?

Explanation / Answer

A)

initial value of ax = 0 m/s2

Initial value of vx = 29.8 m/s

B)

Initial value of at = g = 9.81 m/s2

Initial value of vy = 0 m/s

C)

S= uy*t +0.5 ay*t2

S= 0* 2.6 + 0.5* 9.81*(2.6)2

S = 33.16 m

The building is 33.16 m tall.

D)

S=ux *t +0.5 ax*t2

S= 29.8 *2.6 + 0

S= 77.48 m

The arrow lands 77.48 m from base.

E)

Vy = uy + at = 0 + 9.81 * 2.6 =25.51 m/s

Just before reaching ground, horizontal component of velocity = 29.8 m/s

And vertical component = 25.51 m/s

F)

Angle = tan-1(25.51/29.8)

Angle from horizontal = 40.56 degree

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