Calculating Deceleration and Penetration Distance of Arrow in Styrofoam Block

  • Thread starter Thread starter kinj318
  • Start date Start date
  • Tags Tags
    Block
Click For Summary
SUMMARY

The discussion focuses on calculating the deceleration and penetration distance of an arrow fired into a Styrofoam block. The arrow's initial speed is 22.0 m/s, with a deceleration of 1570 m/s² and the block accelerating at 450 m/s². To determine the time taken for the arrow to stop relative to the block, the formula v = u - a₁t is applicable. Additionally, the common speed of the arrow and block at the moment of stopping can be calculated using the equations of motion for both the arrow and the block.

PREREQUISITES
  • Understanding of kinematic equations
  • Familiarity with acceleration and deceleration concepts
  • Basic knowledge of relative motion
  • Ability to solve equations involving multiple variables
NEXT STEPS
  • Study kinematic equations for uniformly accelerated motion
  • Learn how to apply relative motion principles in physics
  • Explore examples of deceleration calculations in projectile motion
  • Investigate the effects of different materials on penetration depth
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and motion, as well as educators seeking to explain concepts of deceleration and relative motion in practical scenarios.

kinj318
Messages
2
Reaction score
0

Homework Statement


An arrow is fired with a speed of 22.0 m/s at a block of Styrofoam resting on a smooth surface. The arrow penetrates a certain distance into the block before coming to rest relative to it. During this process the arrow's deceleration has a magnitude of 1570 m/s^2 and the block's acceleration has a magnitude of 450 m/s^2.
a)How long does it take for the arrow to stop moving with respect to the block?
b)What is the common speed of the arrow and block when this happens?
c)How far into the block does the arrow penetrate?

Homework Equations


I tried doing a= v/t. to find the time. but the answer wasnt right. i really don't know where to start for it.

The Attempt at a Solution


I need help on parts a and b. i really have no ideas what to do.
 
Last edited:
Physics news on Phys.org
i just need a formula to get going.
 
For arrow, v= u -a1*t. For block, v = 0 + a2*t. You find v and t. Enough?
 

Similar threads

Pulley question -- Two unequal masses hanging by a string
  • · Replies 3 ·
Replies
3
Views
2K
Calculating Friction & Time for a Bullet Penetrating Rubber
  • · Replies 2 ·
Replies
2
Views
2K
Calculating Time for Arrow to Stop Moving Respect to Block
  • · Replies 2 ·
Replies
2
Views
2K
Which block reaches the wall faster?
  • · Replies 2 ·
Replies
2
Views
1K
Body attached to a block by a spring, shaped like an inclined plane
  • · Replies 1 ·
Replies
1
Views
1K
How far into the block does the arrow penetrate?
  • · Replies 9 ·
Replies
9
Views
4K
Bullet shooting vertically into a block
  • · Replies 9 ·
Replies
9
Views
7K
Momentum Problem -- Bullet fired into a block of wood
  • · Replies 2 ·
Replies
2
Views
2K
How far does arrow penetrate into board
  • · Replies 7 ·
Replies
7
Views
7K
Bow & arrow -- Forces on the Bow
  • · Replies 20 ·
Replies
20
Views
4K