To what depth does the bullet penetrate the block in this case?

[Pseudo Statistic]

Hi.
I was trying to solve the following problems, but I just don't understand what principles/laws/concepts I'm supposed to be using.
I hope someone can give me a hint as to where I should start.
Thanks a lot for any replies.

31) Gayle runs at a speed of 4m/s and dives on a sled, initially at rest on the top of a frictionless snow-covered hill. After she has descended a vertical distance of 5m, her brother, who is initially at rest, hops on her back and together they continue down the hill. What is their speed at the bottom of the hill if the total vertical drop is 15m? Gayle's mass is 50kg, the sled has a mass of 5kg, and her brother has a mass of 30kg.

39) A 7g bullet, when fired from a gun into a 1kg block of wood held in a vise, penetrates the block to a depth of 8cm. This block of wood is placed on a frictionless horizontal surface, and a second 7g bullet is fired from the gun into the block. To what depth does the bullet penetrate the block in this case?

48) Consider a frictionless track. A block of mass m1 = 5kg is released from A, 5m in vertical height. It makes a head-on elastic collision at B, at our reference level, with a block of mass m2 = 10kg that is initially at rest. Calculate the maximum height to which m1 rises after the collision.

 

[Doc Al]

31) Gayle runs at a speed of 4m/s and dives on a sled, initially at rest on the top of a frictionless snow-covered hill. After she has descended a vertical distance of 5m, her brother, who is initially at rest, hops on her back and together they continue down the hill. What is their speed at the bottom of the hill if the total vertical drop is 15m? Gayle's mass is 50kg, the sled has a mass of 5kg, and her brother has a mass of 30kg.

You'll need a combination of conservation of energy and conservation of momentum to solve this one. (Hint: Treat the brother jumping on the sled as an inelastic collision.)

39) A 7g bullet, when fired from a gun into a 1kg block of wood held in a vise, penetrates the block to a depth of 8cm. This block of wood is placed on a frictionless horizontal surface, and a second 7g bullet is fired from the gun into the block. To what depth does the bullet penetrate the block in this case?

Assume that the depth of the penetration is proportional to the amount of KE lost in the collision of bullet with block. When the block is free to move, treat the collision as a perfectly inelastic one and calculate the loss of KE.

48) Consider a frictionless track. A block of mass m1 = 5kg is released from A, 5m in vertical height. It makes a head-on elastic collision at B, at our reference level, with a block of mass m2 = 10kg that is initially at rest. Calculate the maximum height to which m1 rises after the collision.

Again, a combination of conservation of energy and conservation of momentum is needed. Hint: Calculate how much KE m1 has after its collision.

 

[Pseudo Statistic]

You'll need a combination of conservation of energy and conservation of momentum to solve this one. (Hint: Treat the brother jumping on the sled as an inelastic collision.)

One question though, how do I model what's given to me initially in terms of energy equations? (The 4m/s and the 5m) Is it 0.5mv^2 + mgh = 0.5mv2^2 where h is 5m, v on the left side is 4m/s and v2 on the right side is unknown?

In 39, how would I proceed to calculating depth afterwards?
Thanks.

 

[Doc Al]

One question though, how do I model what's given to me initially in terms of energy equations? (The 4m/s and the 5m) Is it 0.5mv^2 + mgh = 0.5mv2^2 where h is 5m, v on the left side is 4m/s and v2 on the right side is unknown?

Exactly. Use that to find Gayle's speed just before her brother jumps on the sled.

In 39, how would I proceed to calculating depth afterwards?

Start by figuring out how much KE was required to produce the 8 cm penetration. Then, when you find how much KE was used up in the second case, you can tell how deep the bullet must have penetrated.

 

[Pseudo Statistic]

Exactly. Use that to find Gayle's speed just before her brother jumps on the sled.


Start by figuring out how much KE was required to produce the 8 cm penetration. Then, when you find how much KE was used up in the second case, you can tell how deep the bullet must have penetrated.

Thanks loads for the help, now I can solve these problems. :)