Question

A 100 ton ship traveling at 1000000 miles per hour relative hits a tennis ball sized one pound piece of iron. What is the force generated and what would happen to the ship?

Answer 1

The force generated in 1 second of impact is, F = 201161.37 N

The ship slightly slows down and moves forward with velocity V = 9.9 x 10¹⁰ kg miles/hr

Step-by-step explanation:

Given data,

The mass of the ship, M = 100 ton

= 100,000 kg

The velocity of the ship, V = 1,000,000 miles/hr

The mass of the iron piece, m = 1 lb

= 0.45 kg

The velocity of the iron piece, v = 0

The momentum of the ship,

P = MV

= 100,000 kg x 1,000,000 miles/ hr

= 1 x 10¹¹ kg miles/ hr

The momentum of the iron piece, p = 0

According to the conservation of momentum,

MV + mv = U(M + m)

`U=(MV+mv)/(M+m)`

`U=(1* 10^(11) +0)/(100000+0.45)`

U = 999,995.5 miles/hr

Therefore the momentum of the ship after impact,

P₁ = MU

= 100,000 kg x 999,995.5 miles/hr

= 9.9 x 10¹⁰ kg miles/hr

Therefore, the change in the momentum of the ship,

ΔP = P - P₁

= 1 x 10¹¹ - 9.9 x 10¹⁰

= 449997.98 kg miles/hr

= 201161.37 kg m/s

Let the time period of impact be 1 s

Therefore, the force exerted by the ship on the iron is,

F = ΔP / t

= 201161.37 / 1

= 201161.37 N

Hence, the force generated in 1 second of impact is, F = 201161.37 N

The ship slightly slows down and moves forward with velocity V = 9.9 x 10¹⁰ kg miles/hr