KE is 1/2*m*v^2, 150 = 1/2*m*v^2 Momentum is m*v = 30 so that's two eq with two unknowns. if you express v as 30/m and plug into the KE eq 150 = 1/2*m*(30/m)^2 solve for m, and then use the momentum eq to solve for v

2. by conservation of momentum m1*v1 = m2*v2 so 3.0*v = m2*v/3 rearrange to 3.0*v*3/v = m2 cancel the v and multiply 3.0*3 = 9.0 = m2

3. wow, complicated. first you have to find the time that the block is falling. since the vertical component of acceleration is only due to gravity, distance = 1/2*a*t^2 1.5m = 1/2*9.81*t^2 t=.553 secs

so the horizontal velocity of the block was the horizontal distance traveled divided by the time 2.5m / .553s = 4.52m/s

so now were finally at the conv of momentum problem and m1*v1 = m2*v2 5.5g*v1 = (5.5+22.6) * 4.52 solve for v1, the speed of the dart

4. It appears you have to find the distance that the force is applied thru. since the velocity changes by 8m/s, the average velocity through the collision is (v1+v2)/2 = 14m/s. the distance traveled in 5.0x10^-4s is v*t The energy change was 1/2m1v1^2-1/2m2v2^2. the energy change = force * distance, so force = energy change / distance.