Please Explain One truck is heading east at 80 miles per hour. Its mass is 3000

Question

Please Explain

One truck is heading east at 80 miles per hour. Its mass is 3000 kg. A car (m = 1000kg) is heading north at 40 miles per hour. They collide and stick together. How much energy is lost in the collision? What is the velocity and direction of the car/truck? From the shore of a frozen lake, Eli Manning throws a 2 kg football at a velocity of 20 m/s. A person (m = 30kg) standing on the ice (muk = 0.02) catches the ball. What is their velocity immediately after they catch it? How far do they slide before they come to a stop? One fires a bullet (m=50g) at a block of wood (m=2kg) resting on a frictionless surface. The initial velocity of the bullet is 400m/s. After passing through the block, its velocity is 100m/s. What is the velocity of the block? How much energy is lost? A. A particle of 8 kg with a velocity of 40m/s hits a 40 kg particle that is at. rest. The collision is elastic. What arc the final velocities of the particles? A particle of 8 kg with a velocity of 40m/s al0 degree hits another particle of 25 kg that is moving at a velocity of 70m/s at 90 degree . The collision is elastic. What are the velocities and directions of the particles after the collision?

Explanation / Answer

Final vel in east direction = 80*3000/(3000+1000) = 60 mph

Vel in north direction = 40*1000/4000 = 10 mph

Energy lost = 1/2 * 3000*80^2 + 1/2 * 1000*(40^2) - 1/2 * 4000*(60^2 + 10^2)

= 3*10^6 kg (mi/h)^2

1 mi/hr = 0.44 m/s

So, energy lost = 3*10^6 * 0.44^2

= 599534 J

2) By conservation of momentum, v=2*20/(30+2) = 1.25 m/s

Acceleration due to friction = -uk*g = -0.196 m/s^2

Distance slided = -v^2/2a

= 3.986 m/s

3) momentum lost by bullet = momentum gained by block

0.05*(400-100) = 2*(v-0)

v=7.5 m/s

Energy lost = 1/2 * 0.05*(400^2 - 100^2) - 1/2 * 2*7.5^2

= 18.75 J

4) After an elastic collision,

vel of 8 kg block, v1 = [u1(m1-m2)+2*m2u2]/[m1+m2]

= 40*(8-40)/(40+8)

= -26.67 m/s

vel of 40 kg block, v2 = [u2(m2-m1)+2m1u1] / [m1+m2]

= 2*8*40/48 = 13.33 m/s

5) In the formulae in the above question, use u1=40i, u2 = 70j

m1 = 8 kg, m2 = 25 kg

We get v1 = (-20.61i + 106j) m/s

v2 = (19.39i + 36.06j) m/s

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