College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

An archer shoots an arrow toward a 3.00 × 102-g target that is sliding in her direction at a speed of 2.50 m/s on a smooth, slippery surface. The 22.5-g arrow is shot with a speed of 35.0 m/s and passes through the target, which is stopped by the impact. What is the speed of the arrow after passing through the target?

To determine
Speed of the arrow

Explanation

Given Info: Mass of the arrow is ma=22.5Ã—10âˆ’3â€‰kg , mass of the target is mt=300Ã—10âˆ’3â€‰kg , Velocity towards the archer is negative, initial velocity of the arrow is (va)i=35.0â€‰m/s , initial velocity of the target is (vt)i=âˆ’2.50â€‰m/s , final velocity of the target is (vt)f=0 .

Explanation:

Apply conservation of momentum to arrow-target system

(mava+mtvt)i=(mava+mtvt)f (1)

• ma is the mass of the arrow.
• mt is the mass of the target.
• vt is the velocity of the target.
• va is the velocity of the arrow.

Use 0 for (vt)f in equation (1) to solve (va)f

(mava+mtvt)i=(mava)f(va)f=(mava+mtvt)ima

Substitute 22

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